Answer: 2π√(L/√(g²+a²)).
- A 2π√(L/√(g²+a²))
- B 2π√(L/g)
- C 2π√(L/(g+a))
- D 2π√(L/(g-a))
Correct answer: A. 2π√(L/√(g²+a²))
Explanation: On an accelerating trolley, effective g is the vector sum of g (down) and -a (pseudo-force). g<sub>eff</sub> = √(g²+a²), directed at angle arctan(a/g) from vertical. T = 2π√(L/g<sub>eff</sub>).
In SHM, displacement and velocity are 90° out of phase (v is maximum when x=0, and zero when x is extreme), while acceleration is always exactly opposite in sign to displacement, consistent with a = −ω²x.
Concept context
Simple harmonic motion, spring-mass, pendulum, energy in SHM, and resonance.