Oscillations and waves

What is the period of a simple pendulum of length 1.0 m? What should be its length for
the period to be tripled in value?

• 2 s, 8 m

• 3 s, 6 m

• 2 s, 9 m

• 3 s, 9 m

What changes could you make in a harmonic oscillator that would double the value of
the maximum speed of the oscillating mass?

• Quadruple the spring constant

• Double the spring constant

• Reduce mass to a quarter of its initial value

• Quadruple the mass

A force of 10.5 N is applied to pull a mass attached to a spring with a spring constant of
70 Nm-1. What i s the amplitude of the resulting oscillation?

• 1.5 m

• 0.15 cm

• 1.5 mm

• 0.15 m

A block of mass 920 g is fastened to a spring whose spring constant k is 85 Nm-1. The
spring is pulled a distance of 11 cm from its equilibrium position.
a. What force does the spring exert on the block just before the block is released?
b. What are the angular velocity ω, the frequency f, and the period
T of the resulting oscillation?

• a. 94 N

  b. 8.6 rad/s, 1.53 Hz, 0.85 s

• a. 9.4 N

  b. 9.9 rad/s, 1.73 Hz, 6.5 s

• a. 9.4 N

  b. 9.6 rad/s, 1.53 Hz, 0.65 s

• a. 9.4 N

  b. 9.6 rad/s, 3.53 Hz, 0.56 s

A 4 kg block hangs from a spring extending it 16 cm from its unstretched position.
a. What is the spring constant?
b. What is the frequency of the oscillations?

• 245 N/m, 1.24 Hz

• 24.5 N/m, 0.124 Hz

• 245 N/m, 12.4 Hz

• 24.5 N/m, 1.24 Hz

What is the maximum acceleration of a platform that vibrates with an amplitude of 2.20
cm at a frequency of 6.60 Hz?

• 0.378 m/s²

• 3.78 m/s²

• 378 m/s²

• 37.8 m/s²

A 20 N weight is hung from the bottom of a vertical spring, causing it to stretch 20 cm.
a. What is the spring constant?
b. Calculate the period of the oscillation if the 20N weight is replaced by another
weight of 5N, assuming that the spring is stretched and released from rest.

• 10 N/m, 4.5 s

• 100 N/m, 0.45 s

• 100 N/m, 4.5 s

• 10 N/m, 0.45 s

Find the mechanical energy of a block-spring system having a spring constant of 1.3
N/cm and an amplitude of 2.4 cm.

The end point of a spring vibrates with a period of 2 s when a mass m is attached to
it. When this mass is increased by 2 kg, the period is found to be 3 s. What is the
value of ?

• 1.6 g

• 1.6 kg

• 16 kg

• 0.16 g