Simple Harmonic Motion

A restoring force proportional to the displacement.

12 problems · about 23 minutes · F-TF.B.5, F-IF.B.4

NameDate

Figure — use these to answer the problems

Raise the frequency and the cycles crowd together while the height stays the same. Period and amplitude are independent.

y = 2 cos(1x) + 0

the amplitude2

omega, the angular frequency1

the time shown0

Figure 1

Straightforward practice. Get the method working first.

5 problems

k = 64 and m = 4. What is ω?
Answer
2
Does the period of simple harmonic motion depend on the amplitude?
- No. It depends only on the stiffness and the mass.
- Yes. A larger pull gives a longer period.
k = 16 and m = 1. What is ω?
Answer
k = 45 and m = 5. What is ω?
Answer
ω = 4. What is the period, using 2π as about 6.28?
Answer

The same ideas with more to keep track of.

3 problems

Doubling the amplitude. Does the period change? 1 yes, 0 no.
Answer
A stiffer spring with the same mass. Does the period get longer or shorter? Enter 1 longer, 2 shorter.
Answer
y″ + 25y = 0. What is ω?
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

Sort each change by its effect on the period.
Write each item under the heading it belongs to: A stiffer spring · A lighter mass · Pulling it further before release · Releasing it at a different moment
Makes the period shorter
No effect on the period
y″ + 49y = 0. What is ω?
Answer
The Spring
k = 100 and m = 4. What is ω?
Answer
The Cycle
ω = 2. What is the period, using 2π as about 6.28?
Answer