The maximum speed of a particle executing SHM is 10 m / s and maximum acceleration is 31.4 m / s 2 . Its periodic time is

Question

The maximum speed of a particle executing SHM is 10 m / s and maximum acceleration is 31.4 m / s 2 . Its periodic time is (A) 2 s (B) 4 s (C) 6 s (D) 1 s

Tardigrade Admin · Accepted Answer

Maximum speed, vm=ω A Maximum acceleration, am=ω2 A ∴ (am/vm)=ω=(2 π/T) or (31.4/10)=(2 × 3.14/T) or T=2 s

Q. The maximum speed of a particle executing SHM is $10 m / s$ and maximum acceleration is $31.4 m / s^{2} .$ Its periodic time is

2 s

4 s

6 s

1 s

Maximum speed, $v_{m} = ω A$
Maximum acceleration, $a_{m} = ω^{2} A$
$∴ \frac{a _{m}}{v _{m}} = ω = \frac{2 π}{T}$ or $\frac{31.4}{10} = \frac{2 \times 3.14}{T}$ or $T = 2 s$

Q. The maximum speed of a particle executing SHM is 10m/s and maximum acceleration is 31.4m/s2. Its periodic time is

2 s

4 s

6 s

1 s

Maximum speed, vm​=ωA Maximum acceleration, am​=ω2A ∴vm​am​​=ω=T2π​ or 1031.4​=T2×3.14​ or T=2s

Q. The maximum speed of a particle executing SHM is $10 m / s$ and maximum acceleration is $31.4 m / s^{2} .$ Its periodic time is

Maximum speed, $v_{m} = ω A$
Maximum acceleration, $a_{m} = ω^{2} A$
$∴ \frac{a _{m}}{v _{m}} = ω = \frac{2 π}{T}$ or $\frac{31.4}{10} = \frac{2 \times 3.14}{T}$ or $T = 2 s$