Determine the frequency of the resulting motion.____ Hz Determine the amplitude

Question

Determine the frequency of the resulting motion.____ Hz

Determine the amplitude of the resulting motion.____cm

Determine the phase constant (relative to the original t = 0) of the resulting motion.___ rad

A 1.2 kg block rests on a frictionless surface and is attached to a horizontal spring of constant k = 26 N/m. The block is oscillating with amplitude 15 cm and with phase constant phi = -?/2. A block of mass 0.80 kg is moving from the right at 1.7 m/s. It strikes the first block when the latter is at the rightmost point in its oscillation. The collision is completely inelastic, and the two blocks stick together. Determine the frequency of the resulting motion.____ Hz Determine the amplitude of the resulting motion.____cm Determine the phase constant (relative to the original t = 0) of the resulting motion.___ rad

Explanation / Answer

1)

Here , frequency = (1/2pi)sqrt(k/M)

frequency = (1/2pi)*sqrt(26/(0.8 + 1.2))

frequency =0.57 Hz

the frequency of the resulting motion is 0.57 Hz

ii)

Now , after the collsion , using conservation of momentum ,

(1.2 + 0.8) * v = 1.7 * 0.80

v = 0.68 m/s

Now , using conservation of energy ,

0.5*26 * A^2 = 0.5 * 2 * 0.68^2

A = 0.189 m = 18.9 cm

the amplitude is 18.9 cm

iii)
Now , at time ,t =0

the block have maximum velocity and moving to the left ,

the phase consant = pi = 3.141 rad

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