Oscillations — Previous Year Questions (Class 11 Physics)
Oscillations cover simple harmonic motion and related phenomena. Study equations of motion and energy for mastery of this critical topic.
TL;DR: Oscillations cover simple harmonic motion and related phenomena. Study equations of motion and energy for mastery of this critical topic.
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Oscillations cover simple harmonic motion and related phenomena. Study equations of motion and energy for mastery of this critical topic.
Oscillations — Previous Year Questions with Solutions
Q (2023, 3 marks): A particle undergoes simple harmonic motion with amplitude 5 cm and time period 2 s. Write the equation of motion if the particle starts from the mean position with positive velocity.
Answer: For SHM starting from mean position with positive velocity, the standard form is:
y = A sin(ωt)
where A = 5 cm = 0.05 m is amplitude.
Angular frequency ω = 2π/T = 2π/2 = π rad/s
Therefore:
y = 0.05 sin(πt) m
or y = 5 sin(πt) cm
Final Answer: y = 0.05 sin(πt) m or y = 5 sin(πt) cm
Q (2022, 2 marks): A mass of 2 kg is attached to a spring with spring constant 200 N/m. Calculate the time period of oscillation.
Answer: For a mass-spring system:
T = 2π√(m/k)
where m = 2 kg and k = 200 N/m
T = 2π√(2/200)
T = 2π√(0.01)
T = 2π × 0.1
T = 0.2π ≈ 0.628 s
Final Answer: T = 0.2π s ≈ 0.628 s
Q (2021, 3 marks): At what position in simple harmonic motion is the velocity maximum and the acceleration minimum? Explain with reference to forces.
Answer: In simple harmonic motion:
- Velocity is maximum at the mean position (y = 0), where restoring force is zero
- Acceleration is minimum (zero) at the mean position
At mean position: y = 0, so F = -ky = 0, and a = F/m = 0
At extreme positions (y = ±A): velocity is zero, but acceleration is maximum (magnitude)
- At positive extreme: a = -ωA (negative, pointing toward mean)
- At negative extreme: a = +ωA (positive, pointing toward mean)
The restoring force is zero at mean position but maximum at extremes.
Final Answer: Velocity and acceleration are maximum and minimum respectively at the mean position
Q (2023, 3 marks): A simple pendulum has a time period of 2 s on Earth (g = 10 m/s²). What would be its time period on the Moon where g = 1.6 m/s²?
Answer: For a simple pendulum: T = 2π√(L/g)
On Earth: T_E = 2 s with g_E = 10 m/s²
On Moon: T_M = ? with g_M = 1.6 m/s²
Taking the ratio:
T_M/T_E = √(g_E/g_M)
T_M/T_E = √(10/1.6) = √6.25 = 2.5
T_M = 2.5 × T_E = 2.5 × 2 = 5 s
Final Answer: T_M = 5 s
Q (2022, 5 marks): A particle in SHM has maximum velocity 4 m/s and maximum acceleration 16 m/s². Calculate the amplitude and angular frequency.
Answer: For SHM with amplitude A and angular frequency ω:
Maximum velocity: v_max = ωA = 4 m/s ... (1)
Maximum acceleration: a_max = ω²A = 16 m/s² ... (2)
Dividing equation (2) by equation (1):
(ω²A)/(ωA) = 16/4
ω = 4 rad/s
From equation (1):
A = v_max/ω = 4/4 = 1 m
Verification: a_max = ω²A = 16 × 1 = 16 m/s² ✓
Final Answer: A = 1 m, ω = 4 rad/s
Q (2023, 5 marks): Derive the expression for total energy in simple harmonic motion and show that it remains constant.
Answer: For SHM: x = A sin(ωt)
Velocity: v = dx/dt = Aω cos(ωt)
Kinetic energy: KE = (1/2)mv² = (1/2)mA²ω² cos²(ωt)
Restoring force: F = -kx = -mω²x
Potential energy: PE = (1/2)kx² = (1/2)mω² A² sin²(ωt)
Total energy: E = KE + PE
E = (1/2)mA²ω² cos²(ωt) + (1/2)mω²A² sin²(ωt)
E = (1/2)mA²ω²[cos²(ωt) + sin²(ωt)]
E = (1/2)mA²ω² = (1/2)kA²
Since A, m, ω are constants, E is constant.
Final Answer: Total energy E = (1/2)mω²A² = (1/2)kA² (constant)
Frequently Asked Questions
What is the phase difference between displacement, velocity, and acceleration in SHM?
In SHM: displacement x = A sin(ωt), velocity v = Aω cos(ωt) = Aω sin(ωt + π/2), and acceleration a = -Aω² sin(ωt) = Aω² sin(ωt + π). Phase difference between displacement and velocity is π/2, and between displacement and acceleration is π.
How does damping affect oscillatory motion?
Damping forces (friction, air resistance) oppose motion and gradually reduce the amplitude of oscillation. In underdamped motion, oscillations continue with decreasing amplitude. In critically damped motion, the system returns to equilibrium without oscillating. In overdamped motion, return is slow without oscillation.
More Class 11 Physics PYQs
- Current Electricity
- Ray Optics
- Electrostatics
- Moving Charges and Magnetism
- Electromagnetic Induction
- Alternating Current
🤖 Stuck on any of these? Ask Syllab's free AI Tutor to explain step by step →