# A bunch of MasteringPhysics problems that I don't understand

1. Apr 19, 2005

SHM with torque? Springs and frequency mass relation?

Problem 1

A slender, uniform, metal rod with mass M is pivoted without friction about an axis through its midpoint and perpendicular to the rod. A horizontal spring with force constant k is attached to the lower end of the rod, with the other end of the spring attached to a rigid support.

If the rod is displaced by a small angle Theta from the vertical and released, show that it moves in angular SHM and calculate the period. (Hint: Assume that the angle Theta is small enough for the approximations $${\rm sin} \Theta \approx \Theta$$ and $${\rm cos} \Theta \approx 1$$ to be valid. The motion is simple harmonic if $$d^{2} \theta /dt^{2}= - \omega ^{2} \theta$$ , and the period is then $$T=2 \pi / \omega .$$)

The answer is $$2\pi\sqrt{\frac {M}{3k}}$$

So $$T = 2\pi\sqrt{\frac{m}{k}}$$ usually right? So how do I calculate the period when the spring is giving the force?

Do I use $$\tau = -kx*r$$? But where is r?

Do I need to use the physical pendulum equation and use the 1/12MR^2 equation? But once again, I don't have R. I'm confused on even where to start!

Problem 2:
A partridge of mass 5.10 kg is suspended from a pear tree by an ideal spring of negligible mass. When the partridge is pulled down 0.100 m below its equilibrium position and released, it vibrates with a period of 4.17 s.

I got the speed at equilibrium position (.151 m/s), and the acceleration at .05m above equilibrium (-.113 m/s^2).

This is where I got stuck:
When it is moving upward, how much time is required for it to move from a point 0.050 m below its equilibrium position to a point 0.050 m above it?

The acceleration varies, so do I have to find some type of integral? Or maybe do I take some ratio of the period? I have no idea!

The motion of the partridge is stopped, and then it is removed from the spring. How much does the spring shorten?

Ummm, if the spring is of negligible mass, how do I calculate the amount the spring will shorten? What formula do I use? Argh! This oscillation concept is killing me!

Problem 3:

The scale of a spring balance reading from zero to 200 N is 12.5 cm long. A fish hanging from the bottom of the spring oscillates vertically at 2.60 Hz.

What is the mass of the fish? You can ignore the mass of the spring.

I drew a free-body diagram with $$F_{spring} = m_{fish}*g$$

So the period is .3846 s, and $$k = \frac {m}{(\frac {T}{2\pi})^2}$$.

I tried to find k from some other formula, but I don't know what x to use for $$F = -kx$$ and I have no idea what the 0 to 200 N has to do with this problem. I'm confused again...

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Sorry for posting so much easy problems here, but I don't think my mind is working correctly lately :yuck:. Thanks!

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2. Apr 20, 2005