#1 A spring with spring constant k is suspended vertically from a support and a mass m is attached. The mass is held at the point where the string is not streteched. Then the mass is released and begins to oscillate. The lowest point in the oscillation is 20 cm below the point where the mass was released. What is the oscillation frequency?
#2 A 300g oscillator has a speed of 95.4 cm/s when its displacement is 3 cm and a speed of 71.4 cm/s when its displacement is 6 cm. What is the oscillator's maximum speed.
The Attempt at a Solution
#1 shouldn't be that difficult of a problem, but it's giving me trouble
Here's what I know: amplitude = .20 m
The total energy= 1/2k(.20 m)^2= 1/2m(vmax)^2
But I can't figure out how to substitute the equations into each other to get the correct answer, which is 1.58 Hz
#2 I have also tried substituting the equations into each other:
95.4 cm/s= -omega*A sin (omega*t+phi)
6 cm= Acos(omega*t + phi)
71.4 cm/s = -omega*A sin( omega*t + phi)
Any hints would be greatly appreciated. Thanks.