PROBLEM 1E

All problems refer to the mass–spring configuration depicted in Figure 4.1, page 153.

A 2-kg mass is attached to a spring with stiffness k = 50 N/m. The mass is displaced ¼ m to the left of the equilibrium point and given a velocity of 1 m/sec to the left. Neglecting damping, find the equation of motion of the mass along with the amplitude, period, and frequency. How long after release does the mass pass through the equilibrium position?

Step 1:

In this problem, we need to find the equation of motion of the mass along with the amplitude, period, and frequency.

Step 2:

We gave the mass

Since the mass is displaced .25 m to the left, that means y(0) = -0.25(-1/4) and since at that time, the velocity is

Now the standard form of the equation

We substitute all values in the equation

……………(1)

Now we the auxiliary equation

Which is complex roots of the form

Then the complementary solution.

…………(2)