A block with mass m = 5.1 kg is attached to two springs with spring constants k

Question

A block with mass m = 5.1 kg is attached to two springs with spring constants kleft = 31 N/m and kright = 56 N/m. The block is pulled a distance x = 0.24 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)?

N

2)

What is the effective spring constant of the two springs?

N/m

3)

What is the period of oscillation of the block?

s

4)

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

s

5)

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

m/s

6)

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

m/s2

7)

Where is the block located, relative to equilibrium, at a time 1.02 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)

m

8)

What is the net force on the block at this time 1.02 s? (a negative force is to the left; a positive force is to the right)

N

9)

What is the total energy stored in the system?

J

10)

If the block had been given an initial push, how would the period of oscillation change?

the period would increase

the period would decrease

the period would not change

PLEASE, CLEARLY WORK IT OUT CORRECTLY..THNKS

Explanation / Answer

both spring are in parallel.

1) F = (k1 +k2)x = (31 + 56)*0.24 = 20.88 N

2) effective spring constant = (k1 +k2) = 87 N/m

3) T = 2 x 3.14 x sqrt(5.1/87) = 1.5213 sec

4) t = T/4 = 1.5213/4 = 0.38032 sec

5) v = sqrt[87 x (0.24)2/5.1] = 0.991256 m/s

6) aequilibrium = 0

7) w = sqrt(87/5.1) = 4.1302 rad/s

x = 0.24 sin(wt - /2)

at t= 1.02 s

x = 0.24 sin(4.1302 x 1.02 - /2) = 0.115 m

8) F = 87 x 0.115 = 10.002 N to the left

9) total energy = 0.5 x 87 x (0.24)2 = 2.5056 J

10) the period would not change

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