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.

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

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come closer and become far apart and become steam/gas