A simple harmonic oscillator consists of a block of mass 2.60 kg attached to a s
ID: 2037652 • Letter: A
Question
A simple harmonic oscillator consists of a block of mass 2.60 kg attached to a spring of spring constant 230 N/m. When t = 0.730 s, the position and velocity of the block are x = 0.139 m and v = 3.710 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c)velocity of the block at t = 0 s? A simple harmonic oscillator consists of a block of mass 2.60 kg attached to a spring of spring constant 230 N/m. When t = 0.730 s, the position and velocity of the block are x = 0.139 m and v = 3.710 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c)velocity of the block at t = 0 s?Explanation / Answer
w = sqrt(k / m ) = sqrt(230 / 2.60)
w = 9.4 rad/s
v^2 = w^2 (A^2 - x^2)
3.710^2 = 9.4^2 (A^2 - 0.139^2)
A = 0.418 m .......Ans (Amplitude)
(B) x = A sin(wt + phi)
0.139 = 0.418 sin((9.4 x 0.730) + phi)
6.862 + phi = 6.622
phi = - 0.24 rad
at t = 0
x = 0.418 sin(-0.24) = - 0.10 m .....Ans
(C) v = A w cos(wt + phi)
at t = 0
v = (9.4 x 0.418) cos(-0.24 rad)
v = 3.82 m/s
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