Pendulums
What happens to the period of the pendulum bob if the mass is doubled?
Nothing because mass is not in the equation
At Equilibrium Point: KE and velocity are at ___________________ while UG, spring force, acceleration are ___________.
maximum, minimum
A 3m string of a pendulum is cut in half to a length of 1m. Compare the new period of the pendulum bob to the original period.
It will be square root of 3 times smaller
A block of 4kg is in simple harmonic motion on spring. The block's mass now doubles. How does this change the period of the mass-spring system?
sqrt(2)T
If a mass of 30kg is attached to a vertical spring and it displaces from its original equilibrium 10cm, determine the distance if will travel before it reverses direction if it is released from the original resting position.
20cm or 0.2m
Does the momentum increase or decrease in magnitude as a pendulum goes from its lowest point to its highest point?
Decrease
A spring is stretched by a distance of 10m when a mass with a block of 4kg is attached to it. What is the spring constant? (hint: use Hooke's Law)
Fs=-kx
40=k(10)
k=4 N/m
Find the frequency for a simple pendulum that has a length of 3m and is pulled 2 degrees from equilibrium before it is dropped.
2pi(sqrt(3/10)) = 0.29 Hz
Derive the formula for the spring constant in terms of period of a mass-spring, mass, and other physical constants.
T=2pi(sqrt(m/k))
T2pi=sqrt(m/k)
(T2pi)2=m/k
k=m/(T2pi)2