Figure shows the position-time graph of an object in S.H.M. The correct equation representing this motion is

Question

Figure shows the position-time graph of an object in S.H.M. The correct equation representing this motion is (A) 2 sin ((2 π/5) t+(π/6)) (B) 4 sin ((π/5) t+(π/6)) (C) 4 sin ((π/6) t+(π/3)) (D) 4 sin ((π/6) t+(π/6))

Tardigrade Admin · Accepted Answer

Time period is 12 s from diagram. ω=(2 π/12)=(π/6) Amplitude A=4 Initial phase is determined by putting known values in the equation. 2=4 sin ((π/6) t+φ) sin -1 (1/2)=φ[t=0] (π/6)=φ Hence equation is x=((π/6) t+(π/6))

Q. Figure shows the position-time graph of an object in S.H.M. The correct equation representing this motion is

$2 sin (\frac{2 π}{5} t + \frac{π}{6})$

$4 sin (\frac{π}{5} t + \frac{π}{6})$

$4 sin (\frac{π}{6} t + \frac{π}{3})$

$4 sin (\frac{π}{6} t + \frac{π}{6})$

Q. Figure shows the position-time graph of an object in S.H.M. The correct equation representing this motion is

2sin(52π​t+6π​)

4sin(5π​t+6π​)

4sin(6π​t+3π​)

4sin(6π​t+6π​)

Time period is 12s from diagram. ω=122π​=6π​ Amplitude A=4 Initial phase is determined by putting known values in the equation. 2=4sin(6π​t+ϕ) sin−121​=ϕ[t=0] 6π​=ϕ Hence equation is x=(6π​t+6π​)

$2 sin (\frac{2 π}{5} t + \frac{π}{6})$

$4 sin (\frac{π}{5} t + \frac{π}{6})$

$4 sin (\frac{π}{6} t + \frac{π}{3})$

$4 sin (\frac{π}{6} t + \frac{π}{6})$