Chapter 10 - Simple Harmonic Motion

Question 1

What happens at equilibrium positon? How about at max displacement?

Answer 1

Speed is maximum becuase all the potential energy has been converted to kinetic energy, so KE is also at a max but i thought

At max displacement, velocty zero, acceleration max, and potential energy is max

Question 2

When to use

1) Fapplied = kx
2) F = -kx

Answer 2

1) When you’re applying ofrce to a spring
2) When you’re calculating the restoring force exerted by the spring

Question 3

In a “worst-case” design scenario, a 2000 kg elevator
with broken cables is freely falling from height H when it
first contacts a cushioning spring at the bottom of the
shaft. The spring is supposed to stop the elevator,
compressing d meters as it does so (Figure).
A. In testing the spring a mass of 1000 kg dropped from
height H = 1.6 m compresses it by d = 1.5 m. What is
the spring constant?
B. If the cables break when the elevator is at height
H = 3.2 m above the spring, what would be the
maximum compression of the spring?

Answer 3

A)

You have gravitational potential energy getting converted into spring potential energy. So long as the reference point is chosen as the lowest point of the springs compression.

mgh = 1/2kx^2
with h being 1.6 + 1.5
1000x9.8x3.1 = 1/2k(1.5)^2

B)
Same setup with
mgh = 1/2kx^2
with h being 3.2 + d and x being d then using the quadratic formula to solve for d

Question 4

What is simple harmonic motion?

Answer 4

Repetitive oscillating motion when restoring force acts on object, pulling it to center and getting stronger the more the object moves away