A 0.87-kg mass is attached to the end of a spring and set into oscillation on a

Question

A 0.87-kg 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 passes through the equilibrium position and the position of the mass at any time is shown in the drawing.

Determine the following:

(a) amplitude A of the motion

=____ m

(b) angular frequency

=____ rad/s

(c) spring constant k

=____ N/m

(d) speed of the object at t = 2.0 s

=____ m/s

(e) magnitude of the object's acceleration at t = 2.0 s

=____ m/s2

Explanation / Answer

equation of motion = Asin(wt)

amplitude= 0.1 m

X = 0.1 sin(wt)

time period = 8 sec

2pi/ = 8

angular frequency = 2pi/8 =0.78539816339 s-1

at t= 2 s

dx/dt = 0

speed = 0 m/s

V = Aw cos(wt)

acceleration at t= 2= -Aw^2sin(wt)

= -0.1*^2 = -0.1*0.78539816339^2 =-0.0616850275

= K*A/m (maximum acceleration)

K = m/A *0.0616850275

=0.87 / 0.1 * 0.0616850275

=0.53665973925 N/m

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