A mass of 0.42 kg is attached to a spring and set into oscillation on a horizont

Question

A mass of 0.42 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) = (0.26 m)cos[(10 rad/s)t]. Determine the following. amplitude of oscillation for the oscillating mass m force constant for the spring N/m position of the mass after it has been oscillating for one half a period m position of the mass one-third of a period after it has been released m time it takes the mass to get to the position x = -0.10 m after it has been released s

Explanation / Answer

a )

Amplitude A = 0.26m

b) Force constant

K - m w^2 = (0.42) (10)^2 = 42

c)

Period T = 2 pi /w = 2 pi / 10 = 0.628s

half the period is 0.628 /2 = 0.314s

position

X = 0.26 cos (10 x 0.314 )

X = - 0.26 m

d)

One third the period is t = 0.628 /3 = 0.2093 s

position

X = 0.26 cos (10 x 0.2093 )

X = - 0.13 m

e)

-0.1 = 0.26 cos (10 t )

t = 0.1966s

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