A 0.69 kg mass vibrates according to the equation x=0.50cos6.60t, where x is in

Question

A 0.69 kg mass vibrates according to the equation x=0.50cos6.60t, where x is in meters and t is in seconds

1.

Part A

Determine the amplitude.

Part C
Determine the total energy.
Express your answer using two significant figures.

Part D
Determine the kinetic energy when x = 0.37 m .
Express your answer using two significant figures.

Part E
Determine the potential energy when x = 0.37 m .
Express your answer using two significant figures.

Explanation / Answer

  x(t) = A cos t

A = 0.50 m, =6.60 rad/s

= k/m, m = 0.69 kg, k = 0.69(6.60)² = 30.05 N/m

E = ½ kA² = 0.5(30.05)0.50² = 3.75 J

Employing the Conservation of Energy:

½ mv² + ½ kx² = ½ kA²

and solving for velocity: v

v = k/m A²-x² = 6.60 0.50²-0.37² = 2.21 m/s

Ek = ½ mv² = 0.5*0.69* 2.21² = 1.685 J

Ep = ½ kA² - ½ mv² = 3.75 - 1.685 =2.065 J

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