Class 11 Physics
Oscillations
Acceleration in Simple Harmonic Motion
- Acceleration in uniform circular motion always directed towards the centre. It is known as radial acceleration.
- ap = -ω2r where r = radius
- Consider a particle moving in a circular path. Particle is at some point P at some instant of time, radius of circular path is equal to amplitude.
- Acceleration will be given as
ap = -ω2Awhere
- A = radius of the circle
- (-ive sign shows it is pointing towards the centre of the circle.)
- Consider the acceleration of the projection of the particle P’ on the x-axis.
- Accelerationwill be given as
- a(t) = -ap cosθ
- a(t) = - ap cos(ωt + φ)
- =ω2A cos (ωt + φ)
- a(t) = - ω2x(t) (Using x(t)= A cos (ωt + φ))
To verify expression for acceleration when calculated directly from SHM -
- Displacement in SHM is = A cos (ωt + φ)
- Velocity v(t) in SHM is = -Aw sin (ωt + φ)
Therefore,
- a(t) = dv/dt
- = - ω2A cos (ωt + φ)
- a(t) = - ω2x(t) (Using x(t)= A cos (ωt + φ))
Equation of acceleration of the particle which executesSHM:-
a(t) = - ω2x(t)
We can conclude that:-
- a is proportional to displacement
- acceleration is always directed towards the centre(in circular motion centre is mean position of the SHM)
From above we can say that
- SHM is the projection of the uniform circular motion such that centre of uniform circular motion becomes the mean position of the SHM and the radius of the circular motion is the amplitude of the SHM.
In the above figure we can see that the acceleration, a(t), of the particle P′ is the projection of the acceleration a of the reference particle P.
In all the below graphs displacement, velocity and acceleration all have the same time period T, but they differ in phase.
The acceleration is maximum where velocity is minimum and vice-versa.
Problem: -A body oscillates with SHM according to the equation (in SI units), x = 5 cos [2π t + π/4]
At t = 1.5 s, calculate the (a) displacement,(b) speed and (c) acceleration of the body?
Answer:
The angular frequency ω of the body
= 2π s–1
and its time period T = 1 s.
At t = 1.5 s
(a) Displacement = (5.0 m) cos [(2π s–1)1.5 s + π/4]
= (5.0 m) cos [(3π + π/4)]
= –5.0 x 0.707 m
= –3.535 m
(b) The speed of the body
= – (5.0 m)(2π s–1) sin [(2π s–1) 1.5 s+ π/4]
= – (5.0 m) (2π s–1) sin [(3π + π/4)]
= 10π (0.707) m s–1
= 22 m s–1
(c) The acceleration of thebody
= – (2π s–1)2displacement
= – (2π s-1)2 (–3.535 m)
= 140 m s–2
Problem: -Two identical springs of spring constant k are attached to a block of mass m and to fixed supports as shown in Fig. Show that when the mass is displaced from its equilibrium position on either side, it executes a simple harmonic motion. Find the period of oscillations?
Fig (a)
Answer:-
Let the mass be displaced by a smalldistance x to the right side of the equilibriumposition, as shown in Fig (a). Under thissituation the spring on the left side getselongated by a length equal to x and that onthe right side gets compressed by the samelength. The forces acting on the mass arethen,
F1 = -kx (force exerted by the spring onthe left side, trying to
pull the mass towards the mean position)
F2 = -kx (force exerted by the spring onthe right side, trying to pull the mass towards the mean position)
The net force, F, acting on the mass is thengiven by,
F = –2kx
Therefore, the force acting on the mass is proportional to the displacement and is directedtowards the mean position; therefore, the motion executed by the mass is simple harmonic. The time period of oscillations is given as:-
T=2π√m/2k
Problem:-The acceleration due to gravity on the surface of moon is 1.7 ms–2. What is the time period of a simple pendulum on the surface of moon if its time period on the surface of earth is 3.5 s? (g on the surface of earth is 9.8 ms–2)
Answer: -Acceleration due to gravity on the surface of moon,g' = 1.7 m s–2
Acceleration due to gravity on the surface of earth, g = 9.8 m s–2
Time period of a simple pendulum on earth, T = 3.5 s
T=2π√l/g
where l =length of the pendulum
l= T2/ (2π) 2x g
= (3.5)2/ (4x (3.14)2) x 9.8 m
The length of the pendulum remains constant,
On moon’s surface, time period, T’= 2π√l/g’
=2π ((3.5)2/4x(3.14)2 x 9.8)/1.7
=8.4s
Hence, the time period of the simple pendulum on the surface of moon is 8.4 s.
Problem:-
(a) Time period of a particle in SHM depends on the force constant k and mass m of the particle:
T = 2π√ (m/k). A simple pendulum executes SHM approximately. Why then is the time period of a pendulum independent of the mass of the pendulum?
(b) The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angles of oscillation, a more involved analysis shows that T is greater than 2π√ (l/g)
Think of a qualitative argument to appreciate this result.
(c) A man with a wristwatch on his hand falls from the top of a tower. Does the watch give correct time during the free fall?
(d) What is the frequency of oscillation of a simple pendulum mounted in a cabinthat is freely falling under gravity?
Answer:
(a) For a simple pendulum, force constant or spring factor k is proportional to mass m; therefore, m cancels out in denominator as well as in numerator. That is why the time period of simple pendulum is independent of the mass of the bob.
(b) In the case of a simple pendulum, the restoring force acting on the bob of the pendulum is given as:
F = –mg sinθ
where,
F = Restoring force
m = Mass of the bob
g = Acceleration due to gravity
θ = Angle of displacement
For small θ, sinθ≈θ
For large θ, sinθ is greater than θ.
This decreases the effective value of g.
Hence, the time period increases as:
T = 2π√ (l/g)
(c) Yes, because the working of the wrist watch depends on spring action and it has nothing to do with gravity.
(d) Gravity disappears for a man under free fall, so frequency is zero
Class 11 Physics Oscillations NCERT Chapter 13 Free Notes for Best Revision
Revision of Class 11 Physics Oscillations is a crucial aspect of effective learning. Revision plays a vital role in the learning process and is especially important before exams. Here are some key points you can consider emphasizing in your content:
- Retention and Memory: Regularly reviewing and revisiting the material of Class 11 Physics Oscillations helps reinforce the concepts in students' minds. It strengthens memory pathways, making it easier to recall information during exams and beyond.
- Consolidation of Knowledge: When you revise notes, you are essentially consolidating your knowledge. This means connecting new information with what you already know, making the overall understanding more robust.
- Identifying Knowledge Gaps: Revision allows students to identify any gaps in their understanding or areas where they need further clarification. This gives you a chance to seek help or delve deeper into those topics. For detailed understanding, you can always refer to the videos of Oscillations Class 11 Physics NCERT Chapter 13 on LearnoHub.com
- Building Confidence: As you revise Oscillations Class 11 Physics and become more familiar with the content, your confidence in your abilities grows. Confidence is a crucial factor in exam performance as it reduces anxiety and allows you to approach exams with a positive mindset.
- Different Revision Techniques: Use a variety of revision techniques such as summarizing notes, creating flashcards, practicing past papers, discussing concepts with peers, and teaching others. Different techniques work for different students, and it's essential to find what suits you the best. You can also attend the LIVE Revision classes on LearnoHub.com or watch the LIVE Revision Race videos of LearnoHub on Oscillations Class 11 Physics NCERT Chapter 13.
- Spacing Effect: Spacing out revision sessions over time, rather than cramming all at once, has been shown to improve long-term retention. Create a revision schedule leading up to the exams to allow for spaced practice.
- Regular Revision over Cramming: Regular and consistent revision throughout the academic year is very important. Waiting until the last moment to cram everything can be overwhelming and less effective than spaced-out revision.
- Self-Assessment: Assess your understanding periodically through quizzes or self-tests. This helps you to gauge your progress and identify areas that need further attention. Refer Class 11 Oscillations Online Tests.
- Balanced Approach: Remind students to strike a balance between revision and other activities. Adequate rest, exercise, and relaxation are essential for optimal learning and performance.
- Seeking Help: If you face difficulties during the revision process, Refer the videos of Class 11 Physics Oscillations. Clearing doubts promptly is crucial for a better grasp of the subject matter. You can always ask your doubts on Oscillations Class 11 Physics NCERT Chapter 13. “Ask a Question” section of LearnoHub.com
By highlighting the benefits and strategies of effective revision, you can approach your studies more mindfully and achieve better results in your exams. Best of luck bachhon!
Class 11 Physics seems to be a quite difficult subject for a lot of students. But, if you get a very good conceptual understanding of the subject, it can be very interesting for you.
We, at LearnoHub, will give our best to make Class 11 Physics Oscillations NCERT Chapter 13 super-duper easy for you.
We aim at making learning fun as well as engaging for you with our complete end-end learning content with Oscillations Class 11 Physics Best videos, Notes, NCERT pdf, NCERT complete syllabus, tests and Practice Questions.
Always remember, it is very important to study with full concentration during Revision. Here are a few tips for you on how to revise with full focus:
- Create a Distraction-Free Environment: Find a quiet and comfortable place to study where you can minimize distractions. Turn off or silence your phone, log out of social media accounts, and inform others around you that you need uninterrupted study time. A dedicated study environment will help you focus better.
- Set Specific Goals: Before starting your study session, set clear and achievable goals. Break down your study material into smaller tasks, and plan what you want to accomplish during each session. Having specific goals will give you a sense of direction and purpose, making it easier to concentrate.
- Use the Pomodoro Technique: The Pomodoro Technique is a time management method that involves studying in short, focused intervals, typically 25 minutes, followed by a short break of 5 minutes. After completing four sessions, take a longer break of around 15-30 minutes. This technique can improve focus and productivity by providing regular breaks to recharge.
- Stay Organized: Keep your study materials, notes, and resources well-organized. Having everything you need at hand will save time and reduce distractions caused by searching for materials. Use color-coded folders or digital tools to maintain a structured study system.
- Practice Mindfulness and Meditation: Before you begin studying, take a few minutes to practice mindfulness or meditation. Deep breathing exercises and clearing your mind of distractions can help you approach your study session with a calm and focused mindset.
Remember, studying with full concentration is a skill that takes time and practice to develop. If you find your mind wandering during study sessions, gently bring your focus back to the task at hand and be patient with yourself. With consistent effort, you can improve your ability to concentrate and make the most of your study time.
Last but not the least, To get the best hold on Class 11 Physics Oscillations Book Chapter 13. Do not forget to check out:
- Oscillations Class 11 Physics Best videos
- Oscillations Class 11 Physics NCERT Solutions
- Class 11 Physics Oscillations Revision notes
- Oscillations Class 11 Physics DPPS, Download PDF of solutions
- Class 11 Physics Oscillations Online Tests
- Class 11 Physics Sample papers
