A couple waves questions that my class can't get

[Sny]

A mass of 0.39 kg connected to a light spring with a spring constant of 22.2 N/m oscillates on a frictionless horizontal surface. If the spring is compressed 4.0 cm and released from rest, determine the following.

(a) the maximum speed of the mass

(b) the speed of the mass when the spring is compressed 1.5 cm

(c) the speed of the mass when the spring is stretched 1.5 cm

(d) For what value of x does the speed equal one-half the maximum speed?


When four people with a combined mass of 280 kg sit down in a car, they find that the car drops 1.00 cm lower on its springs. Then they get out of the car and bounce it up and down. What is the frequency of the car's vibration if its mass (empty) is 2.0 x 10^3 kg?

I don't even know where to start on these, so all I'm asking for is a nudge in the right direction, possibly some formulas or reading material.

 

[Curious3141]

A mass of 0.39 kg connected to a light spring with a spring constant of 22.2 N/m oscillates on a frictionless horizontal surface. If the spring is compressed 4.0 cm and released from rest, determine the following.

(a) the maximum speed of the mass

(b) the speed of the mass when the spring is compressed 1.5 cm

(c) the speed of the mass when the spring is stretched 1.5 cm

(d) For what value of x does the speed equal one-half the maximum speed?


When four people with a combined mass of 280 kg sit down in a car, they find that the car drops 1.00 cm lower on its springs. Then they get out of the car and bounce it up and down. What is the frequency of the car's vibration if its mass (empty) is 2.0 x 10^3 kg?

I don't even know where to start on these, so all I'm asking for is a nudge in the right direction, possibly some formulas or reading material.

These are problems dealing with simple harmonic motion (s.h.m.) and springs. You'll need to read up on those.

Actually all the formulae you will need are :

$$\ddot x = -\omega^2 x$$ (s.h.m.)

$$F = -kx$$ (springs)

Find out what those formulae mean, and we'll go from there.

 

[clive]

(a) I suggest to use the law of energy conservation: in all points of the trajectory, the total energy must be the same:
(1) $$E=\frac{1}{2}mv^2+\frac{1}{2}kx^2=const.$$
I suggest to apply Eq. (1) between the extreme point and the middle one.

(b, c, d) play with Eq. (1) for different points of the trajectory and show us what you obtain!


For the second problem, try to find the equivalent elastic constant of the car suspension with
(2) $$Mg=kx$$
and then the frequence of oscillations with
(3) $$2\pi \nu=\sqrt{\frac{k}{m}}$$
($$M$$-combined mass of people, $$m$$ - mass of the car without people)