Question

In: Physics

A 0.770-kg mass attached to a vertical spring of force constant 147 N/m oscillates with a...

A 0.770-kg mass attached to a vertical spring of force constant 147 N/m oscillates with a maximum speed of 0.322 m/s. Calculate the period related to the motion of the mass. Calculate the amplitude. Calculate the maximum magnitude of the acceleration.

Expert Solution

The angular frequency of the oscillation is,

w = [k / m]^1/2

= [147 N/m / 0.770 kg]^1/2

= 13.8 rad/s

Thus, the period of the oscillation is,

T = 2(pi)/w

= 2(pi) / (13.8 rad/s)

= 0.4547 s

= 0.45 s

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The amplitude of the oscillation is,

A = v_max/ w

= 0.322 m/s / 13.8 rad/s

= 0.023 m

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Maximum acceleration is,

a_max = w²A

= (13.8 rad/s)²(0.023 m)

= 4.44 m/s²

genius_generous answered 3 months ago

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