# Working with two springs placed in series.

a 3-lb block can slide without friction in a slot and is connected to two springs of constant k_1=80 lb/ft and k_2=6 lb/ft. The springs are initially unstreatched when the block is pulled 2 in. to the right and released.Determine (a) the maximum velocity of the block, (b)the velocity of the block when it is 0.8 in. from its initial position.

See attached for diagram.

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Consider two springs placed in series with a mass on the bottom of the second. The force is the same on each of the two springs. Therefore

(1)

Solving for in terms of ,

(2)

We are looking for the effective spring constant so that

(3)

Where is the total displacement of the mass. Equating (3) with the right side of (1) and ...

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