1) A spring-block system sits on a horizontail, frictionless surface. The blocks

Question

1) A spring-block system sits on a horizontail, frictionless surface. The blocks mass is 5.00 kg and the mass of the spring is negligible. The spring is compressed to 30.0 cm from its equilibrum position and released frin rest at time 0.00s. The block then undergoes simple harmonic motion. A physic student measures the time it takes for the spring to be streched out to 12.5 cm from its initial release as 0.150s. Determine the spring constant.

2) A transverse sinusodial wave on a sting has a period T=0.130s and travels in the +x direction with a speed of 23.1 m/s. The ampitude of the wave is 8.50 cm. At t=0.00s, and element of the string at x=1.50m is traveling downward at a speed of 0.584 m/s. Determine the displacement (cm) of a string element at x=1.8m at time t=3.50s (Note: the phase angle is not zero!)

Explanation / Answer

1) x = A cos(wt)

at t = 0.150 s, x = 12.5 cm

12.5 = 30 cos(wt)

w t = cos^-1(12.5 / 30) = 0.363 pi

w = 0.363 pi / 0.150 = 7.61 rad/s

and m w^2 = k

k = 5 x 7.61^2 = 289.3 N/m

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