A simple harmonic oscillator consists of a block of mass 2.90 kgattached to a sp

Question

A simple harmonic oscillator consists of a block of mass 2.90 kgattached to a spring of spring constant 150 N/m.When t =1.50 s, the position and velocity of the block are x =0.188 m and v =3.930 m/s. (a) Whatis the amplitude of the oscillations? What werethe (b) positionand (c) velocityof the block at t =0 s?

Explanation / Answer

m = 2.90 kg, k = 150 N/m. t =1.50 s, x =0.188 m, v =3.930 m/s. total energy E = kx2/2 + mv2/2 = 25.0 J (a) Whatis the amplitude of the oscillations? E = kA2/2 A = (2E/k) = 0.578 m What were the (b) positionand (c) velocityof the block at t = 0s? x = Acos(t + ), v = -Asin(t + ), t = 1.50 s, = (k/m) = 7.192 rad/s x > 0, v > 0, so cos(t + ) >0, sin(t + ) < 0, t + is in 4th quadrant. tan(t + ) = -v/(x) = -2.91 tan(7.192*1.50 + ) = -2.91 7.192*1.50 + = arctan(-2.91) = 2 - 1.24 = 5.04 rad = -5.745 rad at t = 0, x = Acos = 0.496 m v = -Asin = -2.13 m/s

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