Question

A block with mass m = 5.7 kg is attached to two springs with
spring constants k_{left} = 36 N/m and k_{right} =
53 N/m. The block is pulled a distance x = 0.22 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/s^{2}

7)

Where is the block located, relative to equilibrium, at a time 0.91 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 0.91 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

Answer #1

spring constant K-left ( for spring on left) = 36 N/m

spring constant K-right ( for spring on right) = 53 N/m

mass of block, m = 5.7 kg

initial displacement, x = 0.22 m to the left

a. Initial net force = Force by right spring + Force by left
spring (RIght one is pull and left one is push, so both add up in
the right direction)

F = (K-right + K-left)*x = (36+53)0.22 = 19.58 N ( to the
right)

b. Effective spring constant be k

kx = 19.58N = k*0.22

k = 89 N/m

c. Period of osscillation = T

angular frequency = w

frequency of osscilation = f

for spriong mass system , w = sqroot(k/m)

and T = 1/f

and w = 2*pif

so, T = 2pi*sqroot(m/k) = 2*pi*sqroot(5.7/89) = 0.66601 s

d. BLovck takes T/4 time to reachequilibrium position for the first
time it is released from rest

so, time taken , t = T/4 = 0.16650 s

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