## A mass weighing 32 pounds stretches a spring 2 feet. Determine the amplitude and period of motion if the mass is initially released from a p

Question

A mass weighing 32 pounds stretches a spring 2 feet. Determine the amplitude and period of motion if the mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of 6 ft/s.

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5 months 2021-08-22T05:58:17+00:00 1 Answers 67 views 0

## Answers ( )

1. A mass weighing 32 pounds stretches a spring 2 feet.

(a) Determine the amplitude and period of motion if the mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of 6 ft/s.

(b) How many complete cycles will the mass have completed at the end of 4 seconds? Period = seconds

8 cycles

Explanation:

A mass weighing 32 pounds stretches a spring 2 feet;

it implies that the mass (m) = m= = 1 slug

Also from Hooke’s Law

2 k = 32

k = k = 16 lb/ft

Using the function:  (because of the initial position being above the equilibrium position) ( as a result of upward velocity)

NOW, we have: However; means  also implies that:  Hence,      Period can be calculated as follows:

= = seconds

How many complete cycles will the mass have completed at the end of 4 seconds?

At the end of 4 seconds, we have:   cycles