Question

The equation of motion for an oscillating particle is given by $x=3sin\left(4\pi t\right)+4cos\left(4\pi t\right)$, where x is in mm and t is in second

• A. The motion is simple harmonic
• B. The period of oscillation is 0.5 s
• C. The amplitude of oscillation is 5 mm
• D. The particle starts its motion from the equilibrium

Answer 1

Answer: (A), (B), (C)

The correct options are
A The period of oscillation is 0.5 s
B The motion is simple harmonic
C The amplitude of oscillation is 5 mm

$\left(A\right)x=5\sin (4\pi t+\arctan (4/3\left)\right)$ so motion is simple harmonic
$\left(B\right)T=2\pi /4\pi =0.5$
$\left(C\right)x=5\sin (4\pi t+\arctan (4/3\left)\right)$ so amplitude is $5mm$
$\left(D\right)$ at $t=0,x\ne 0$ so false