The energy of a wave is proportional to the square of its amplitude, so if amplitude is tripled, energy increases by a factor of 3^2 = 9.

The time period T is given by T = 2π/ω. Therefore, T = 2π/5 = 0.4 s.

A damping ratio greater than 1 indicates overdamped behavior in the system.

The time period T is inversely proportional to the frequency f. If the frequency is doubled, the time period halves.

Period T = 1/f, if frequency is halved, period doubles.

Wavelength is inversely proportional to frequency; if frequency is doubled, wavelength is halved.

Wavelength is inversely proportional to frequency; if frequency is doubled, wavelength halves.

According to the wave equation v = fλ, if frequency (f) is doubled and speed (v) remains constant, the wavelength (λ) must halve.

The speed of a wave is given by the product of its frequency and wavelength (v = fλ). If the frequency is doubled, the wavelength must be halved to keep the speed constant.

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

Damped frequency (ω_d) = ω_n√(1-ζ^2) = 5√(1-0.2^2) = 5√(0.96) ≈ 4.8 rad/s.

Frequency f = v/λ = 300 m/s / 3 m = 100 Hz.

Total energy (E) = (1/2)m(v_max)^2. Solving for v_max gives v_max = sqrt(2E/m) = sqrt(2*50/2) = 10 m/s.

In constructive interference, the amplitudes of the waves add up, resulting in a doubled amplitude.

Constructive interference results in a wave of higher amplitude.

Constructive interference occurs when two waves meet in phase, resulting in a wave with a larger amplitude.

The damping ratio can be calculated using the logarithmic decrement method, leading to ζ = 0.25.

In a damped harmonic oscillator, increasing the damping coefficient results in a decrease in the amplitude of oscillation over time.

The time period of a damped harmonic oscillator remains the same; damping affects amplitude, not period.

Damping ratio (ζ) = c / (2√(mk)). If m is doubled, ζ is halved.

Increasing the damping coefficient results in a decrease in amplitude over time, leading to quicker energy loss.

In a damped harmonic oscillator, the amplitude of oscillation decreases over time due to energy loss.

The damping coefficient determines how quickly the energy is lost in a damped harmonic oscillator.

In a damped harmonic oscillator, the amplitude decreases over time due to the energy lost to damping forces.

In a damped harmonic oscillator, the amplitude decreases over time due to the loss of energy.

The damping coefficient determines the rate of energy loss in a damped harmonic oscillator.

The damping coefficient determines how quickly energy is lost in a damped harmonic oscillator.

Using E(t) = E_0 e^(-2ζω_nt), we find ζ = 0.2.

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

Ratio = driving frequency / natural frequency = 5 Hz / 4 Hz = 1.25.