The position of a 50g oscillating mass is given by x ( t )=( 2.0cm )cos 11 t , w

Question

The position of a 50g oscillating mass is given byx(t)=( 2.0cm )cos 11 t, where t is in seconds.

Part A

Determine the amplitude.

Express your answer using two significant figures.

Part B

Determine the period.

Express your answer using two significant figures.

Part C

Determine the spring constant.

Express your answer using two significant figures.

Part D

Determine the maximum speed.

Express your answer using two significant figures.

Part E

Determine the total energy.

Express your answer using two significant figures.

Part F

Determine the velocity at t = 4.5

Explanation / Answer

as for simple harmonic motion ,

x(t) = A * cos( w*t)

here , x(t) = 2 * cos(11 t) cm

A)

comparing ,

A = 2 cm

amplitude is 2 xm

B)

as w = 11 rad/s

time period , T = 2pi/w

time period , T = 2pi/11

time period , T = 0.571 s

the time period is 0.571 s

C)

as w = sqrt(k/m)

11 = sqrt(k/.050)

solving for k

k = 6.05 N/m

the spring constant is 6.05 N/m

D)

Vmax = A*w

Vmax = 0.02 * 11

Vmax = 0.22 m/s

the maximum speed is 0.22 m/s

E)

total energy = 0.5 * m * Vmax^2

total energy = 0.5 * 0.050 * 0.22^2

total energy = 1.21 *10^-3 J

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