This and the following two questions relate to the same situation: A 3 kg block
ID: 1390766 • Letter: T
Question
This and the following two questions relate to the same situation:
A 3 kg block is attached to a massless spring and oscillates back and forth with simple harmonic motion according to the equation x(t) = 4cos(5t), where x is in meters and t is in seconds. What is the spring constant of the spring?
(a) 43 N/m
(b) 12 N/m
(c) 75 N/m
(d) 20 N/m
(e) 60 N/m
QUESTION 9*
What is the maximum velocity of the block?
(a) 5 m/s
(b) 20 m/s
(c) 70 m/s
(d) 100 m/s
(e) 150 m/s
QUESTION 10*
Now suppose the amplitude of the oscillation is doubled. How will the period of oscillation change?
(a) The period will be doubled.
(b) The period will be halved.
(c) The period will be unchanged.
Explanation / Answer
8)
m=3kkg
x(t)=4*cos(5t)
compare this equation with x(t)=A*cos(wt)
then
amplitude A=4 m
angula velocty w=5 rad/sec
now,
w=sqrt(k/m)
k=m*w^2
k=3*5^2
= 75 N/m ..option C is correct
9)
Vmax=A*w
=4*5
=20 m/sec ....option b is correct
10)
the correct option is,(c)
The period will be unchanged.
the time period not depends on amplitude