Write an equation that relates the distance d of the object from its rest position after t seconds.

Question

An object of mass m (in grams) attached to a coiled spring with damping factor b (in grams per second) is pulled down
a distance a (in centimeters) from its rest position and then released. Assume that the positive direction of the motion is up and the period is T (in seconds) under simple harmonic motion.

(a) Write an equation that relates the distance d of the object from its rest position after t seconds.
(b) Graph the equation found in part (a) for 5 oscillations using a graphing utility.

m = 25,    a = 10,     b = 0.7,       T = 5

Answer 1

Step 1:

(a)

The displacement of the object at is .

The damping factor .

Mass of the object is .

The time period .

Time Period .

The displacement by an oscillating object from rest position at time secs is

Substitute the values , , and in the above equation.

Step 2:

(b)

Graph the function .

Graph the function for 5 oscillations.

Solution:

(a) The displacement by an oscillating object is .

(b) Graph of the displacement of the object for 5 oscillations is