A particle in SHM has an amplitude of 20 cm and time period of 2 sec. Its maximum velocity will be(in m/s):
$0.04 π^{2}$
$0.2 π$
$0.2 π^{2}$
$0.04 π$

Question

A particle in SHM has an amplitude of 20 cm and time period of 2 sec- Its maximum velocity will be-in m-s-0-04  pi-20-2  pi0-2  pi-20-04  pi

Toppr Admin · Accepted Answer

-v-dxdt-A-x3C9-cos-x3C9-t-x3B8-Maximum v occurs for maximum value of-cos-x3C9-t-x3B8- which is 1Thus- maximum-v-A-x3C9-Now- -x3C9-2-x3C0-T-2-x3C0-2-x3C0-and A-20cm-0-2mThus- maximum v - 0-2-x3C0-

A particle in SHM has an amplitude of 20 cm and time period of 2 sec. Its maximum velocity will be(in m/s):0.04 π20.2 π0.2 π20.04 π

v=dxdt=Aωcos(ωt+θ)Maximum v occurs for maximum value of cos(ωt+θ), which is 1Thus, maximum v=AωNow, ω=2πT=2π2=π, and A=20cm=0.2mThus, maximum v = 0.2π

A particle in SHM has an amplitude of 20 cm and time period of 2 sec. Its maximum velocity will be(in m/s):
$0.04 π^{2}$
$0.2 π$
$0.2 π^{2}$
$0.04 π$

$v = \frac{d x}{d t} = A ω c o s (ω t + θ)$
Maximum $v$ occurs for maximum value of $c o s (ω t + θ)$ , which is 1
Thus, maximum $v = A ω$
Now, $ω = \frac{2 π}{T} = \frac{2 π}{2} = π$ , and $A = 20 c m = 0.2 m$
Thus, maximum v = $0.2 π$