A block with mass m = 5.6 kg is attached to two springs with spring constants k

Question

A block with mass m = 5.6 kg is attached to two springs with spring constants kleft = 36 N/m and kright = 52 N/m. The block is pulled a distance x = 0.21 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 0.89 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 0.89 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

Explanation / Answer

a) the magnitude of the net force on the block is,

F = [kleft + k right]x = (36+52)*0.21 = 18.48 N

b)  the effective spring constant is.

Keff = kleft + k right = 36+ 52 = 88 N/m

c) the period of oscillation is,

T= 2*pi*sqrt[m/k] = 2*pi*sqrt(5.6/88) = 1.585 s

d) the required time is

T/4 =1.585 / 4 = 0.39625 s = 0.396 s

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