A mass of 0.38 kg Is attached to a spring and set into oscillation on a horizont

Question

A mass of 0.38 kg Is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.30 m)cos[(10 rad/s)t]. Determine the following. (a) amplitude of oscillation for the oscillating mass (b) force constant for the spring (c) position of the mass after it has been oscillating for one half a period (d) position of the mass one-third of a period after it has been released (e) time it takes the mass to get to the position x = -0.10 m after it has been released How can you determine the time for the oscillating mass to get to a specific position from an expression for the position of the object at any time?

Explanation / Answer

x= 0.3 cos(10t)

-0.1=0.3 cos 10t

-1/3 = cos 10t

cos-1 (-1/3)= 10(rad/s)t

1.91 rad= 10 (rad/s) t

t= 1.91/10 s

t=0.191 s

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