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 stretched position. The position of the mass at any time is described by x = (6.7 cm) cos [2pit/(0.67 s)]. Determine the following. (Where applicable, indicate the direction with the sign of your answer. Assume the mass is initially stretched in the positive direction.) period T of the motion s location of the mass at t = 3.0 s cm location of the mass at t = 3.0 s + T cm

Explanation / Answer

a. Here, position of the mass,

x= 6.7 cos[2*pi*t/.67]

Comparing it to simple harmoic mation equation,

x= A cos(wt) = A cos(2*pi*t/T)

w= angular frequency, T = time period

T =0.67 s

b. Location of the mass, t=3 s

x= 6.7 cos[2*pi*3/0.67]

= 6.7 cos(28.11) =6.7*(-0.987)

=6.61 cm

(c) t =3+T=3.67

x= 6.7 cos[2*pi*3.67/0.67]

= 6.7 cos(34.39.11) =6.7*(-0.987)

=6.61 cm

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