Question

Part A:

The position of a 55 g oscillating mass is given by x(t)=(2.0cm)cos(10t), where t is in seconds. Determine the velocity at t=0.40s.

Express your answer in meters per second to two significant figures.

Part B:

Assume that the oscillating mass described in Part A is attached to a spring. What would the spring constant k of this spring be?

Express your answer in newtons per meter to two significant figures.

Part C:

What is the total energy E of the mass described in the previous parts?

Express your answer in joules to two significant figures.

Answer 1

The position of oscillating mass is given by

Velocity of the function

Time t=0.40

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Part B

Angular frequency in simple harmonic function [x(t)=Acos(wt)]

so

m=55g=0.055kg

Squaring both sides

N/m

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Part C

From the position function

maximum amplitude can be given by

Total energy of mass

(KE=0 at maximum x_max because velocity is zero)

J