Increasing the amplitude of the driving force generally increases the amplitude of the oscillation in a forced system.

Energy is proportional to the square of the amplitude, so if amplitude is doubled, energy increases by 2^2 = 4 times.

Maximum amplitude occurs when the driving frequency is equal to the natural frequency.

In forced oscillations, the amplitude is directly proportional to the driving force in the steady state.

Ratio = driving frequency / natural frequency = 2 / 1.5 = 1.33

When the driving frequency matches the natural frequency, resonance occurs, leading to maximum amplitude.

When the driving frequency matches the natural frequency, resonance occurs, leading to maximum amplitude.

Increasing the amplitude of the driving force generally increases the amplitude of the forced oscillation.

At resonance, the driving frequency matches the natural frequency of the system, leading to a significant increase in amplitude.

The maximum amplitude achieved at resonance is referred to as the resonance peak.

In a harmonic oscillator, the total mechanical energy is the sum of kinetic and potential energy, which remains constant over time.

Total energy E is proportional to the square of the amplitude. If amplitude is halved, energy is reduced to 1/4, hence it halves.

The total energy in simple harmonic motion is proportional to the square of the amplitude. If the amplitude increases, the total energy increases.

The phase constant φ depends on the initial conditions of the motion, such as the initial position and velocity.

The period (T) increases with mass (T = 2π√(m/k)).

The period T is given by T = 2π√(m/k). If m increases, T increases.

Acceleration is always opposite to displacement in SHM, hence 180 degrees.

In SHM, the restoring force is directly proportional to the displacement from the mean position.

In simple harmonic motion, the restoring force is directly proportional to the displacement from the mean position.

The velocity is maximum at the mean position where the displacement is zero.

The period T = 2π√(m/k) increases with an increase in mass (m).

Maximum speed (v_max) = ωA. Thus, ω = v_max/A = 4/2 = 2 rad/s.

In a standing wave, the points of maximum displacement are called antinodes, while nodes are points of zero displacement.

The distance between two consecutive nodes in a standing wave is λ/2.

A node is a point in a standing wave where the displacement is always zero.

Nodes in a standing wave are points where there is no displacement, meaning they are points of minimum amplitude.

In a standing wave, nodes are points of zero amplitude, while antinodes are points of maximum amplitude.

'A' represents the amplitude of the wave, which is the maximum displacement from the equilibrium position.

The energy of a wave is proportional to the square of its amplitude, so if the amplitude increases, the energy increases with the square of the amplitude.

The energy carried by a wave is proportional to the square of its amplitude, so if the amplitude increases, the energy increases with the square of that increase.