Exploring Simple Harmonic Motion

What is the formula for the period of a mass-spring system?

• T = m/k

• T = 2π(m/k)

• T = √(k/m)

• T = 2π√(m/k)

How does the mass of an object affect the oscillation of a spring?

• Decreased mass leads to a longer oscillation period and lower frequency.

• Increased mass leads to a longer oscillation period and lower frequency.

• Increased mass results in a shorter oscillation period and higher frequency.

• Mass has no effect on the oscillation period or frequency of a spring.

Describe the motion of a simple pendulum. What factors influence its period?

• The period of a simple pendulum is influenced by its length and the acceleration due to gravity.

• The period is only influenced by the mass of the pendulum.

• The period is constant regardless of the pendulum's length.

• The period is determined solely by the angle of release.

What is the relationship between the length of a pendulum and its period?

• The period of a pendulum decreases with the length of the pendulum.

• The period of a pendulum is constant regardless of its length.

• The length of a pendulum has no effect on its period.

• The period of a pendulum increases with the length of the pendulum.

Explain the concept of potential and kinetic energy in simple harmonic motion.

• Kinetic energy is always zero in SHM.

• Potential energy is constant throughout the motion.

• Both potential and kinetic energy are maximum at the extremes.

• In SHM, potential energy is maximum at the extremes of motion and kinetic energy is maximum at the equilibrium position.

How is total mechanical energy conserved in a mass-spring system?

• Mechanical energy is not conserved due to external forces acting on the mass.

• Kinetic energy is lost as potential energy increases in the system.

• Total mechanical energy is conserved as the sum of kinetic and potential energy remains constant in a mass-spring system.

• Total mechanical energy increases as the spring compresses.

What is damping in oscillations, and what are its effects on the motion?

• Damping increases the amplitude of oscillations by adding energy.

• Damping is the process of amplifying oscillations to create more intense motion.

• Damping is the reduction of oscillation amplitude due to energy loss, affecting motion by decreasing intensity and altering frequency.

• Damping has no effect on the frequency of oscillations.

Differentiate between underdamped, critically damped, and overdamped systems.

• Overdamped: oscillates with increasing amplitude

• Critically damped: oscillates with constant amplitude

• Underdamped: returns to equilibrium slowly with oscillation

• Underdamped: oscillates with decreasing amplitude; Critically damped: returns to equilibrium quickly without oscillation; Overdamped: returns to equilibrium slowly without oscillation.

What is resonance, and how can it be both beneficial and harmful?

• Resonance is the phenomenon of increased amplitude of oscillation at specific frequencies, which can be beneficial in applications like music and communication, but harmful in structures due to potential failure.

• Resonance is a type of sound that cannot be measured or observed.

• Resonance always leads to structural failure and should be avoided.

• Resonance is only a musical term with no practical applications.

Provide an example of resonance in everyday life.

• A person singing in the shower.

• A dog barking at a passing car.

• A swing being pushed at the right moments.

• A car engine running smoothly.