IIT JEE Physics Practice Paper – Oscillations and SHM (Set 23)

Instructions

Total Questions: 20 | Marks: 4 each | No Negative Marking

Q1. Simple harmonic motion is:

Periodic motion
Circular motion
Random motion
Translational motion

Q2. Restoring force in SHM is proportional to:

Displacement
Velocity
Acceleration
Mass

Q3. Equation of SHM restoring force:

F = -kx
F = kx
F = ma
None

Q4. Time period of spring-mass system:

2π√(m/k)
2π√(k/m)
√(m/k)
None

Q5. Frequency is reciprocal of:

Time period
Velocity
Amplitude
Displacement

Q6. Angular frequency relation:

ω = 2πf
ω = f/2π
ω = T/2π
None

Q7. Maximum displacement in SHM is:

Amplitude
Frequency
Velocity
Period

Q8. Velocity in SHM is maximum at:

Mean position
Extreme position
Everywhere same
None

Q9. Acceleration in SHM is maximum at:

Extreme position
Mean position
Zero everywhere
None

Q10. Total energy in SHM is proportional to:

A²
A
1/A
√A

Q11. Potential energy in SHM is maximum at:

Extreme position
Mean position
Midpoint
None

Q12. Kinetic energy in SHM is maximum at:

Mean position
Extreme position
Everywhere same
None

Q13. Phase difference in one complete oscillation:

2π
π
π/2
4π

Q14. Simple pendulum time period formula:

2π√(L/g)
2π√(g/L)
√(L/g)
None

Q15. Time period of simple pendulum depends on:

Length
Mass
Amplitude only
Density

Q16. SHM projection is obtained from:

Uniform circular motion
Linear motion
Random motion
Projectile motion

Q17. Unit of frequency:

Hertz
Joule
Newton
Watt

Q18. Displacement equation of SHM:

x = Asinωt
x = vt
x = at²
None

Q19. Mechanical energy in ideal SHM remains:

Constant
Increasing
Decreasing
Zero

Q20. SHM acceleration is directed toward:

Mean position
Extreme position
Tangential direction
None

Submit

Oscillations and Simple Harmonic Motion – IIT JEE Notes (Set 23)

Introduction to Oscillations

Definition

Oscillatory motion is the repeated to-and-fro motion of a body about its mean equilibrium position.

Examples

Simple pendulum, vibrating spring, tuning fork, and oscillating particles.

Periodic Motion

Definition

Motion that repeats itself after equal intervals of time is called periodic motion.

Time Period

The time taken to complete one full oscillation.

Frequency

Number of oscillations completed in one second.

Relation

f = 1/T

Simple Harmonic Motion (SHM)

Definition

SHM is a special type of oscillatory motion in which restoring force is directly proportional to displacement and directed toward mean position.

Restoring Force Equation

F = -kx

Key Insight

Negative sign shows restoring force acts opposite to displacement.

Characteristics of SHM

Main Features

Motion is periodic, acceleration is variable, and restoring force always acts toward equilibrium position.

Symmetry

Motion is symmetric about mean position.

Displacement Equation of SHM

Equation

x = A sin(ωt + φ)

Variables

A = amplitude

ω = angular frequency

φ = phase constant

Amplitude

Definition

Maximum displacement of particle from mean position.

Importance

Determines maximum energy of oscillating particle.

Angular Frequency

Formula

ω = 2πf

Relation with Time Period

ω = 2π/T

Velocity in SHM

Formula

v = ω√(A² – x²)

Maximum Velocity

v_max = Aω

Key Insight

Velocity is maximum at mean position and zero at extreme positions.

Acceleration in SHM

Formula

a = -ω²x

Maximum Acceleration

a_max = Aω²

Key Insight

Acceleration is maximum at extreme positions and zero at mean position.

Energy in SHM

Total Energy

E = ½kA²

Kinetic Energy

Maximum at mean position.

Potential Energy

Maximum at extreme positions.

Conservation of Energy

Total mechanical energy remains constant in ideal SHM.

Phase in SHM

Definition

Phase specifies the state of oscillation of a particle at any instant.

Phase Difference

Difference in phase between two oscillating particles.

Complete Oscillation

Phase change in one complete oscillation is 2π radians.

Spring-Mass System

Time Period Formula

T = 2π√(m/k)

Variables

m = mass attached

k = spring constant

Key Insight

Heavier mass increases time period while stiffer spring decreases it.

Simple Pendulum

Definition

A small bob suspended by light inextensible string oscillating under gravity.

Time Period Formula

T = 2π√(L/g)

Variables

L = length of pendulum

g = acceleration due to gravity

Key Insight

Time period is independent of mass of bob.

Conditions for Simple Pendulum SHM

Small Angle Approximation

Oscillations must have small angular displacement.

Reason

For small angles, sinθ ≈ θ.

Projection of Uniform Circular Motion

Concept

SHM can be considered as projection of uniform circular motion on diameter.

Importance

Helps derive displacement, velocity, and acceleration equations.

Damped Oscillations

Definition

Oscillations whose amplitude gradually decreases due to friction or resistance.

Examples

Real pendulum and vibrating tuning fork.

Forced Oscillations

Definition

Oscillations produced by external periodic force.

Example

Vibrating machine parts.

Resonance

Definition

When frequency of external force equals natural frequency of system, amplitude becomes maximum.

Applications

Musical instruments, radio tuning, bridges.

Quality Factor

Definition

Measures sharpness of resonance.

Key Insight

Higher quality factor means lower energy loss.

Important Graphs in SHM

Displacement-Time Graph

Sinusoidal graph representing periodic motion.

Velocity-Time Graph

Velocity leads displacement by phase π/2.

Acceleration-Time Graph

Acceleration is opposite in phase to displacement.

Conceptual Insights

Key Understanding

In SHM, restoring force always tries to bring particle back to equilibrium position.

Common Mistakes

Students often confuse velocity and acceleration positions and forget phase relationships.

Important Exam Concepts

Conceptual Traps

Velocity is maximum at mean position while acceleration is zero there.

JEE Strategy

Practice SHM equations, energy concepts, pendulum numericals, and phase relations thoroughly for IIT JEE problems.