Hooke's Law and Oscillations Quiz

According to Hooke's law, the force exerted by a spring on an object is proportional to

• the mass of the object.

• the displacement of the spring.

• the length of the spring.

• the volume of the object.

Answer explanation

According to Hooke's law, the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position, making 'the displacement of the spring' the correct choice.

In any system in simple harmonic motion, the restoring force acting on the mass in the system is proportional to

• displacement.

• the length of a pendulum.

• the mass.

• frequency.

Answer explanation

In simple harmonic motion, the restoring force is always proportional to the displacement from the equilibrium position. This means that as the object moves further from equilibrium, the force acting to bring it back increases.

The spring constant in a given oscillating mass-spring may be changed by

• increasing the mass.

• decreasing the mass.

• decreasing the initial displacement.

• none of the above

Answer explanation

The spring constant is a property of the spring itself and is not affected by the mass or displacement. Therefore, changing the mass or displacement does not change the spring constant, making 'none of the above' the correct choice.

In an oscillating mass-spring system, the velocity of the mass is greatest when the mass is

• at the point of maximum displacement.

• halfway between the equilibrium point and maximum displacement.

• at the point where acceleration is greatest.

• at the equilibrium point.

Answer explanation

In an oscillating mass-spring system, the velocity is greatest at the equilibrium point because the mass has maximum kinetic energy there, while at maximum displacement, the velocity is zero.

The period of a pendulum may be decreased by

• shortening its length.

• increasing the mass of the bob.

• moving its equilibrium point.

• decreasing the mass of the bob.

Answer explanation

The period of a pendulum is determined by its length. Shortening the length decreases the period, while changing the mass or moving the equilibrium point does not affect the period significantly.

As the swinging bob of a pendulum moves farther from its equilibrium position, the pendulum's _____ increases.

• frequency

• mass

• restoring force

• length

Answer explanation

As the pendulum bob moves away from its equilibrium position, the distance from equilibrium increases, leading to a greater restoring force acting to bring it back. Thus, the restoring force increases.

The gravitational potential energy of the bob of a swinging pendulum is at its maximum when the bob is at

• maximum displacement.

• the equilibrium point.

• the center of its swing.

• minimum displacement.

Answer explanation

The gravitational potential energy of the bob is highest at maximum displacement, where it is farthest from the equilibrium point. At this position, the bob has the greatest height, resulting in maximum potential energy.

Stretching a spring increases its _____ energy.

• mechanical kinetic

• gravitational potential

• vibrational kinetic

• elastic potential

Answer explanation

Stretching a spring stores energy in the form of elastic potential energy. This energy is due to the deformation of the spring, which can be released when the spring returns to its original shape.

What happens to an oscillating mass-spring system as a result of damping?

Answer explanation

Damping in an oscillating mass-spring system causes the amplitude of oscillations to decrease over time, leading to a gradual loss of energy until the system eventually comes to rest.

What is the spring constant of a spring that stretches a distance of 8.5 cm when a mass of 370 g is hung on it?

Answer explanation

To find the spring constant (k), use Hooke's Law: F = kx. Here, F = mg = 0.37 kg * 9.81 m/s² = 3.627 N, and x = 0.085 m. Thus, k = F/x = 3.627 N / 0.085 m = 42.7 N/m.