A mass is attached to the end of a spring and set into oscillation on a horizont

Question

A mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a compressed position. The record of time is started when the oscillating mass first passes through the equilibrium position, and the position of the mass at any time is described by x = (4.7 cm)sin[(7.9 rad/s)t].

Determine the following:

(a) frequency of the motion

=____ Hz

(b) period of the motion

=____ s

(c) amplitude of the motion

=____ cm

(d) first time after t = 0 that the object reaches the position x = 2.6 cm

=____ s

Explanation / Answer

x = (4.7 cm)sin[(7.9 rad/s)t]

w = 7.9 * = 2**f

=> f = 3.95 Hz

w = 2*/T

T = 0.2532 sec

amplitude of motion A = 4.7 cm

d)

2.6 = 4.7sin(7.9*pi*t)

0.1866*pi = 7.9*pi*t

=> t = 0.02362 sec

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