15.1 Simple Harmonic Motion

What conditions must be met to produce SHM?

Give an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude.

As you pass a freight truck with a trailer on a highway, you notice that its trailer is bouncing up and down slowly. Is it more likely that the trailer is heavily loaded or nearly empty? Explain your answer.

Prove that using $x \left(t\right) = A \text{sin} \left(\omega t + \phi\right)$ will produce the same results for the period for the oscillations of a mass and a spring. Why do you think the cosine function was chosen?

If your heart rate is 150 beats per minute during strenuous exercise, what is the time per beat in units of seconds?

A stroboscope is set to flash every $8.00 \times 10^{−5} \text{s}$. What is the frequency of the flashes?

Each piston of an engine makes a sharp sound every other revolution of the engine. (a) How fast is a race car going if its eight-cylinder engine emits a sound of frequency 750 Hz, given that the engine makes 2000 revolutions per kilometer? (b) At how many revolutions per minute is the engine rotating?

A mass $m_{0}$ is attached to a spring and hung vertically. The mass is raised a short distance in the vertical direction and released. The mass oscillates with a frequency $f_{0}$. If the mass is replaced with a mass nine times as large, and the experiment was repeated, what would be the frequency of the oscillations in terms of $f_{0}$ ?

How much leeway (both percentage and mass) would you have in the selection of the mass of the object in the previous problem if you did not wish the new period to be greater than 2.01 s or less than 1.99 s?