This lesson includes 1 additional question and 24 additional question variations for subscribers.

# Lesson Worksheet: Simple Harmonic Motion Mathematics

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

**Q1: **

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?

- A s
- B s
- C s
- D s
- E s

**Q2: **

A mass on a spring oscillates with a period of 0.8 s and an amplitude of 8 cm. At , 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 ?

- A cm/s
- B cm/s
- C cm/s
- D cm/s
- E cm/s

**Q3: **

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.

- A m
- B m
- C m
- D m
- E m

**Q4: **

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

- A
- B
- C
- D
- E

**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.

- A s
- B4 s
- C3 s
- D s
- E6 s

Find the maximum speed of the particle.

- A cm/s
- B4 cm/s
- C cm/s
- D cm/s
- E cm/s

Find the maximum acceleration of the particle.

- A cm/s
^{2} - B4 cm/s
^{2} - C cm/s
^{2} - D cm/s
^{2} - E cm/s
^{2}

**Q6: **

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

- A
- B
- C
- D

**Q7: **

A particle vibrates along the 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: **

The displacement of a particle as a function of time is given by , where is measured in meters and 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.

- A
- B
- C
- D
- E

**Q9: **

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

- 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

**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.

- A
- B
- C
- D
- E