# Worksheet: Simple Harmonic Motion

In this worksheet, we will practice modeling the motion of an object having an acceleration toward a point proportional to its displacement from that point.

**Q1: **

An object undergoing simple harmonic motion has a frequency of 5.5 Hz and an amplitude of 4.5 mm. What is the speed of the object when it is at its equilibrium position?

**Q2: **

The bob of a simple pendulum moves from a point that intersects the line , which is one of the bob’s positions of maximum displacement, to a point that intersects the line , which is the bob’s other position of maximum displacement. The bob moves between these points in 0.25 s. What is the frequency of the bob’s simple harmonic motion?

**Q3: **

An object in simple harmonic motion has a frequency of 2.5 Hz. The maximum displacement of the object from its equilibrium position has a magnitude of 1.5 cm. What is the magnitude of the acceleration of the object when it is at its greatest displacement?

**Q4: **

The diagram shows plots of how the values of four quantities change relative to each other with time.

If the green plot corresponds to the displacement of an object in simple harmonic motion from its equilibrium position, which plot corresponds to the object’s velocity?

- AOrange
- BGreen
- CPink
- DBlue

If the pink plot corresponds to the displacement of an object in simple harmonic motion from its equilibrium position, which plot corresponds to the object’s velocity?

- ABlue
- BOrange
- CGreen
- DPink

If the orange plot corresponds to the displacement of an object in simple harmonic motion from its equilibrium position, which plot corresponds to the object’s velocity?

- AOrange
- BGreen
- CBlue
- DPink

If the blue plot corresponds to the displacement of an object in simple harmonic motion from its equilibrium position, which plot corresponds to the object’s velocity?

- AGreen
- BBlue
- COrange
- DPink

If the orange plot corresponds to the acceleration of an object in simple harmonic motion, which plot corresponds to the object’s velocity?

- AGreen
- BPink
- COrange
- DBlue

If the pink plot corresponds to the acceleration of an object in simple harmonic motion, which plot corresponds to the object’s velocity?

- ABlue
- BPink
- COrange
- DGreen

**Q5: **

An object that is initially at rest in its equilibrium position for simple harmonic motion is set into simple harmonic motion, taking negligible time, with an initial speed of 18 cm/s. The simple harmonic motion has a frequency of 2.8 Hz. What is the amplitude of the motion?

**Q6: **

An object in simple harmonic motion has a frequency of
1.5 Hz. The magnitude of the acceleration of the
object when it is at its greatest
displacement is 2.4 m/s^{2}.
What is the magnitude of the maximum displacement of the
object from its equilibrium position?

**Q7: **

An object in simple harmonic motion with a frequency of 3.75 Hz has a maximum magnitude of displacement from its equilibrium position of 2.25 cm. The object is initially at rest when it is released at its positive maximum displacement. What is the displacement of the object 0.125 s after it is released?

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

**Q8: **

The diagram shows plots of how the values of displacement of an object in simple harmonic motion change relative to each other with time.

Which plot has a phase difference of rad from the blue plot?

- AOrange
- BPink
- CBlue
- DGreen

Which plot has a phase rad ahead of the blue plot?

- APink
- BGreen
- COrange
- DBlue

Which plot has a phase rad behind the blue plot?

- APink
- BGreen
- CBlue
- DOrange

Which plot has a phase rad ahead of the green plot?

- ABlue
- BOrange
- CGreen
- DPink

Which plot has a phase rad behind the orange plot?

- AOrange
- BBlue
- CGreen
- DPink

**Q9: **

An object in simple harmonic motion with a frequency of 1.35 Hz has a maximum magnitude of displacement from its equilibrium position of 3.33 cm. The object is initially at rest when it is released at its positive maximum displacement.

What is the time interval between the object being released and it having a displacement of 1.45 cm from its equilibrium position?

What is the time interval between the object being released and it having a displacement of cm from its equilibrium position?

**Q10: **

What is the total distance, in meters, moved in 80 s by an object undergoing simple harmonic motion that has an amplitude of 1.4 cm and a frequency of 3.2 Hz?