A harmonic oscillator consists of a block attached to a spring (k = 400 N/m). Th

Question

A harmonic oscillator consists of a block attached to a spring (k = 400 N/m). The mass is initially displaced to x_max = 0.128 m. At some later time, t, the block has the following kinematic variables: x = 0, 100 m, v = -13.6 m/s, a = -123 m/s^2 a) find the frequency of oscillation b) the mass of the block c) the amplitude of the motion. d) and the total mechanical energy of the system. A pendulum that consists of a brass disk of radius, r = 15.00 cm, and mass of 1.000 kg. The disk is attached to a thin rod of negligible mass. The period of the pendulum is 2.000 s for small oscillations. L = 83.06 cm. Compute the acceleration due to gravity round off to 4 digits.

Explanation / Answer

1) k = 400 N/m

xmax = A = 0.128 m

x =A cos(wt)

x = 0.128cos(wt)

0.1 = 0.128 cos(wt) ..(1)

v = dx/dt

v =-Awsin(wt)

-13.6 = -0.128*w*sin(wt)

a = dv/dt

a = -Aw^2sin(wt)

-123 = -w^2*x

123 = w^2*0.1

w = 35.07 rad/s

w = 2pi*f =35.07

f = 5.58 Hz

(b) w^2 =k/m

35.07 =400/m

m = 11.41 kg

(c) A = 0.128 m

(d) E = 0.5kA^2

E = 0.5*400*0.128^2

E = 3.3 J

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