A simple harmonic oscillator consists of a block ofmass 4.20 kg attached to aspr

Question

A simple harmonic oscillator consists of a block ofmass 4.20 kg attached to aspring of spring constant 194 N/m.When t = 3.00 s, the position and velocity of the blockare x =+0.129 m and v = +3.415 m/s. (a) What is the amplitude of the oscillations?
m

(b) What was the position of the mass at t = 0s?
x = m

(c) What was the velocity of the mass at t = 0s?
v = m/s (a) What is the amplitude of the oscillations?
m

(b) What was the position of the mass at t = 0s?
x = m

(c) What was the velocity of the mass at t = 0s?
v = m/s

Explanation / Answer

(a) total energy of system E=1/2*k*A2=1/2*k*0.1292+1/2*4.2*3.4152 => amplitude A= 0.519 m (b)x=A*sin(t+) v=A*cos(t+) A2=x2+(v/)2 => = 6.796 rad/s when t=3 s 0.129=0.519*sin(t+) => t+=14.40 =14.4-88.2=-73.8 =14.4-88.2=-73.8 => when t=0 ; =-73.8 => x=-0.498 m (c) velocity   v=A*cos()=0.984 m/s (c) velocity   v=A*cos()=0.984 m/s

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