IIT JEE Physics Practice Paper – SHM & Oscillations (Set 10)

Instructions

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

Q1. Time period of SHM is:

T = 2π/ω
T = ω/2π
T = ω²
None

Q2. Acceleration in SHM is:

Proportional to displacement
Constant
Zero
Random

Q3. Maximum velocity occurs at:

Mean position
Extreme
Anywhere
None

Q4. Maximum acceleration occurs at:

Extreme position
Mean position
Anywhere
None

Q5. Frequency is:

1/T
T
T²
None

Q6. Energy in SHM is:

Constant
Increasing
Decreasing
Zero

Q7. Kinetic energy maximum at:

Mean position
Extreme
Both
None

Q8. Potential energy maximum at:

Extreme
Mean
Both
None

Q9. Angular frequency ω is:

2πf
f/2π
1/f
None

Q10. SHM restoring force is:

-kx
kx
Zero
Constant

Q11. Spring time period is:

2π√(m/k)
2π√(k/m)
√(m/k)
None

Q12. Pendulum time period is:

2π√(l/g)
2π√(g/l)
l/g
None

Q13. Phase difference unit:

Radian
Meter
Joule
None

Q14. SHM graph is:

Sinusoidal
Linear
Parabolic
None

Q15. Amplitude is:

Maximum displacement
Minimum displacement
Average
None

Q16. SHM velocity is zero at:

Extreme
Mean
Both
None

Q17. SHM acceleration zero at:

Mean
Extreme
Both
None

Q18. SHM is example of:

Periodic motion
Linear motion
Random motion
None

Q19. Total energy in SHM ∝

Amplitude²
Frequency
Velocity
None

Q20. SHM occurs due to:

Restoring force
Constant force
Zero force
None

Submit

Simple Harmonic Motion (SHM) & Oscillations – IIT JEE Notes (Set 10)

Simple Harmonic Motion (SHM)

Definition

Simple Harmonic Motion is a type of periodic motion in which the restoring force is directly proportional to displacement and acts towards the mean position.

Restoring Force

F = -kx

The negative sign indicates that the force is always directed towards the equilibrium position.

Basic Equations of SHM

Displacement

x = A sin(ωt + φ)

Velocity

v = ω√(A² – x²)

Acceleration

a = -ω²x

Time Period and Frequency

Time Period

T = 2π/ω

Frequency

f = 1/T

Angular Frequency

ω = 2πf

Energy in SHM

Total Energy

E = (1/2)kA²

Total energy remains constant throughout the motion.

Kinetic Energy

Maximum at mean position and zero at extreme positions.

Potential Energy

Maximum at extreme positions and minimum at mean position.

Important Positions in SHM

Mean Position

Displacement = 0, velocity is maximum, acceleration is zero.

Extreme Position

Displacement = maximum, velocity is zero, acceleration is maximum.

Spring-Mass System

Time Period

T = 2π√(m/k)

Key Insight

Time period depends on mass and spring constant, not on amplitude.

Simple Pendulum

Time Period

T = 2π√(l/g)

Important Point

Valid only for small oscillations.

Phase and Phase Difference

Phase

Represents the state of oscillation at any instant.

Unit

Radian

Phase Difference

Difference in phase between two oscillating particles.

Graphical Representation

Displacement-Time Graph

Sinusoidal curve.

Velocity-Time Graph

Also sinusoidal but shifted by π/2.

Acceleration-Time Graph

Opposite phase to displacement.

Characteristics of SHM

Periodic Motion

Motion repeats after equal time intervals.

Oscillatory Nature

Motion occurs about a fixed mean position.

Important Relationships

Maximum Velocity

vₘₐₓ = ωA

Maximum Acceleration

aₘₐₓ = ω²A

Energy Relation

Total energy ∝ Amplitude²

Conceptual Insights

Key Understanding

Velocity and acceleration are not constant. Both vary continuously during motion.

Common Mistakes

Students often assume acceleration is maximum at mean position, which is incorrect.

Important Exam Concepts

Conceptual Traps

Time period of SHM does not depend on amplitude. Frequency remains constant for given system.

JEE Strategy

Focus on formulas, graphs, and understanding relation between displacement, velocity, and acceleration.