Section 3.9: Mixed Practice
This section provides mixed practice problems covering simple harmonic motion, damped & forced oscillations, resonance, and waves. Attempt these problems to reinforce your understanding.
- A pendulum of length 2 m is released from 10° angle. Find its period and maximum speed.
- A mass-spring system with k = 150 N/m and m = 3 kg is displaced by 0.2 m. Find maximum acceleration and velocity.
- A damped oscillator loses 5% of energy per cycle. If initial energy is 10 J, find energy after 4 cycles.
- A wave with frequency 5 Hz travels 20 m in 4 s. Determine wavelength and speed.
- Two waves of amplitude 0.1 m and same frequency interfere constructively. Find resultant amplitude.
- A 0.5 kg mass attached to a spring (k = 80 N/m) oscillates. Find its angular frequency and period.
- Compute the resonance frequency for a system with m = 2 kg and k = 200 N/m.
- A mass-spring system is oscillating with amplitude 0.15 m. Find the maximum kinetic energy.
- A 0.2 m long pendulum oscillates. Calculate its frequency if g = 9.8 m/s².
- Two waves of frequency 10 Hz and amplitude 0.05 m interfere destructively. Find resultant amplitude.