Worksheet: Simple Harmonic Motion

In this worksheet, we will practice analyzing the simple harmonic motion of an object.

Q1:

A mass on a spring oscillates with a period of 0.8 s and an amplitude of 12 cm. At 𝑡=0s, it is 6 cm to the left of equilibrium and moving to the left. What is the position of the mass at time 𝑡=2s?

  • A12 cm to the right of equilibrium
  • B24 cm to the right of equilibrium
  • C3 cm to the right of equilibrium
  • D10 cm to the right of equilibrium
  • E6 cm to the right of equilibrium

Q2:

A particle is moving along a straight line with simple harmonic motion. Its maximum acceleration is 10 ms−2 and its maximum speed is 3 ms−1. Calculate the amplitude of the motion.

  • A910 m
  • B94 m
  • C310 m
  • D95 m
  • E920 m

Q3:

A particle 𝑃 of mass 0.4 kg is moving along a straight line with simple harmonic motion. The distance between 𝑃 and a fixed point 𝑂 on the line is 𝑥 meters at 𝑡 seconds. The force acting on 𝑃 has a magnitude of 10𝑥 and acts in the direction opposite to the motion. Find the period of the motion.

  • A2𝜋5
  • B𝜋10
  • C𝜋5
  • D4𝜋5

Q4:

A 6 kg mass attached to a spring is observed to oscillate with a period of 3 s. What is the period of oscillation if a 8 kg mass is attached to the spring?

  • A3 s
  • B23 s
  • C32 s
  • D43 s
  • E53 s

Q5:

A particle of mass 15 g moves in simple harmonic motion with a frequency of 3 Hz and an amplitude of 4 cm.

Determine the period of the motion.

  • A13 s
  • B4 s
  • C3 s
  • D14 s
  • E6 s

Find the maximum speed of the particle.

  • A48𝜋 cm/s
  • B4 cm/s
  • C12𝜋 cm/s
  • D24𝜋 cm/s
  • E22𝜋 cm/s

Find the maximum acceleration of the particle.

  • A144𝜋 cm/s2
  • B4 cm/s2
  • C72𝜋 cm/s2
  • D24𝜋 cm/s2
  • E124𝜋 cm/s2

Q6:

A simple harmonic oscillator takes 15 s to undergo five complete vibrations. Find the angular frequency in radians per second.

  • A2𝜋3
  • B𝜋3
  • C2𝜋15
  • D5𝜋3
  • E4𝜋3

Q7:

A particle vibrates along the 𝑥-axis with a frequency of 5 Hz. Determine the time taken by the particle to reach the maximum positive displacement eleven times, starting from the equilibrium position while moving in the positive direction.

Q8:

A mass on a spring oscillates with a period of 0.8 s and an amplitude of 8 cm. At 𝑡=0s, it is 4 cm to the left of equilibrium and moving to the left. What is the magnitude of the velocity of the mass at time 𝑡=2s?

  • A53𝜋 cm/s
  • B10𝜋 cm/s
  • C203𝜋 cm/s
  • D103𝜋 cm/s
  • E5𝜋 cm/s

Q9:

The displacement of a particle 𝑃 as a function of time is given by 𝑥=3(2𝜋𝑡+5𝜋)cos, where 𝑥 is measured in meters and 𝑡 in seconds.

Determine the period of the motion.

  • A2 s
  • B4 s
  • C1 s
  • D0.25 s
  • E0.5 s

Determine the amplitude of the motion.

Determine the phase constant.

  • A5𝜋
  • B3𝜋
  • C2𝜋
  • D10𝜋
  • E0.5𝜋

Q10:

A spring stretches by 4.9 cm when a 10 g mass is hung from it. Calculate the period of motion when a 20 g mass attached to this spring oscillates in simple harmonic motion.

  • A𝜋4
  • B𝜋5
  • C𝜋2
  • D2𝜋5
  • E𝜋10

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