A block with mass m = 4.5 kg is attached to two springs with spring constants k

Question

A block with mass m = 4.5 kg is attached to two springs with spring constants kleft = 36 N/m and kright = 49 N/m. The block is pulled a distance x = 0.25 m to the left of its equilibrium position and released from rest.

1-What is the magnitude of the net force on the block (the moment it is released)?

2-What is the effective spring constant of the two springs?

3-What is the period of oscillation of the block?

4-How long does it take the block to return to equilibrium for the first time?

5-What is the speed of the block as it passes through the equilibrium position?

6-What is the magnitude of the acceleration of the block as it passes through equilibrium?

7-Where is the block located, relative to equilibrium, at a time 0.88 s after it is released? (if the block is left of equilibrium give the answer as a negative value; if the block is right of equilibrium give the answer as a positive value)

8-What is the net force on the block at this time 0.88 s? (a negative force is to the left; a positive force is to the right)

9-What is the total energy stored in the system?

Explanation / Answer

the springs are parallel so

net force = (kleft + kright) * x

net force = (36 + 49) * 0.25

net force = 21.25 N

effective spring constant = kleft + kright

effective spring constant = 36 + 49

effective spring constant = 85 N/m

time period = 2 * pi / sqrt(k/m)

time period = 2 * pi / sqrt((kleft + kright)/m)

time period = 2 * pi / sqrt(85/4.5)

time period = 1.44569 sec

time it'll take to return to equlibrium = time period / 4 because its already at one of it extremes

time it'll take to return to equlibrium = 1.44569 / 4

time it'll take to return to equlibrium = 0.3614 sec

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