SHM block on a string questions

[novelized]

Homework Statement

A block of unknown mass is attached to a spring with a spring constant of 8.3 N/m and undergoes simple harmonic motion with an amplitude of 12.0 cm/s. For the block, calculate its:

a) mass,

b) period of motion,

c) maximum acceleration and

d) energy.


I can calculate b, c, and d once I find the mass but I have no idea how to find the mass. In all of the equations, you either need to know the displacement or acceleration in order to find mass :/

2. While visitng friends at Cal State Chico, you pay a visit to the Crazy Horse Saloon. This fine establishment features a 200-kg mechanical bucking bull, that has a mechanism that makes it move vertically in simple harmonic motion. Whether the "bull" has a rider or not, it moves with the same amplitude (0.250 m) and frequency, 1.50 Hz. After watching other saloon patrons hold on to the "bull" while riding, you (mass 75 kg) decide to ride it the macho way by not holding on. No one is terribly surprised when oy come out of the saddle. Later, while waiting for your bruises and pride to heal, you ponder over the fact that you leave the saddle when the "bull" is moving upward and decide to pass the time by calculating the following:

a) What is the magnitude of the downward acceleration of the saddle when you lose contact?

b) How high is the top surface of the saddle above its equilibrium position when you first become airborne?

c) How fast are you moving upward when you leave the saddle?

d) You are in free fall until you return to the saddle. Show that this (returning the saddle) happens 0.538 s later.

e) What is your speed relative to the saddle at the instant you return?

For a, could I assume that the downward acceleration is 9.8 m/s^2? For b, I used the equation for position, x(t) = Acost(wt + phi) and took the second derivative and set it to 9.8 m/s^2, since your acceleration becomes equal to g as soon as you become airborne. Is this correct? If b is correct, then I know how to find c. For d, I set ut+.5at^2 = Acos(wt + phi), since I thought the displacement of the person and the saddle would be the same in .538 s. Is that assumption correct?

Thank you.

 

[Fightfish]

1. Consider the lowest point of the motion of the spring-mass system. Then,

$$a = - \omega^{2}x$$

$$\frac{kx-mg}{m} = -\frac{k}{m}x$$​

Since you know k and x, you can solve for m.