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/s²

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