A particle with a mass of 0.690 kg is attached to a horizontal spring with a for

Question

A particle with a mass of 0.690 kg is attached to a horizontal

spring with a force constant of 6.21 N/m. At the moment t =

0, the particle has its maximum speed of 7.5 m/s and is moving to

the left. (Assume that the positive direction is to the right.) (a)

Determine the particle's equation of motion, specifying its

position as a function of time. (Use the following as necessary:

t.)

x =

(b) Where in the motion is the potential energy three times the

kinetic energy?

±

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"text" />

m

(c) Find the minimum time interval required for the particle to

move from x = 0 to x = 1.00 m. (Be sure to enter the

minimum time and not the total time elapsed.)

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"text" />

s

(d) Find the length of a simple pendulum with the same

period.

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"text" />

m

Explanation / Answer

a) mv^2/2 = kx^2/2

0.690 x 7.5^2 = 6.21A^2

A = 2.5 m

w = sqrt(k/m) =

x = 2.5m sin(3t + pi/2 )

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