Question

1. A mass is attached to a horizontal spring, and oscillates with a period of 1.2 s and with an amplitude of 14 cm. At t = 0 s, the mass is 14 cm to the right of the equilibrium position.

a) Write down the function for the position, velocity, and acceleration of the mass as a function of time. The only variable you should have in your expressions is time. Make sure you indicate the units for each function.

b) Plot of the position vs time and velocity vs time from 0 s to 2.4 s. On each plot, make sure you label the period, initial value and amplitude.

c) What is the distance traveled between t = 0.3 s and t = 1.6 s?
Hint: If you are not sure how to answer this problem, the graph of position vs time from part b)

may be useful.

d) At what position (or positions) is the speed of the block two-thirds of the maximum speed?

Hint: You do not need the mass or the spring constant to solve this. Solve this problem using energy considerations, and recall that ω = ?k/m → k = mω2. You can calculate the maximum speed from the information you have.

Answer 1