The time period of oscillation of a S-H-O- is dfrac-pi -2- s- Its acceleration a phase angle dfrac-pi -3- rad from extreme position is 2 m-s-2- what is its velocity a displacement equals to half of its amplitude from mean position-0-707 m-s0-866 m-ssqrt-2- m-ssqrt-3- m-s

Question

Toppr Admin · Accepted Answer

A-x3C9-2xx-Acos-x3C0-3-x3C9-2-x3C0-TT-x3C0-2-x3C9-42-4T2-xD7-A-xD7-12-A-14V-x3C9-xD7-x221A-A-2-x2212-x2x-A2V-x3C9-A-xD7-x221A-32V-0-866m-sec

The time period of oscillation of a S.H.O. is π2 s. Its acceleration at a phase angle π3 rad from extreme position is 2 m/s2, what is its velocity at a displacement equals to half of its amplitude from mean position?0.707 m/s0.866 m/s√2 m/s√3 m/s

a=ω2xx=Acosπ3ω=2πTT=π2ω=42=(4T2×A×12)A=14V=ω×√(A)2−x2x=A2V=ωA×√32V=0.866m/sec

$a = ω^{2} x$
$x = A c o s \frac{π}{3}$
$ω = \frac{2 π}{T}$
$T = \frac{π}{2}$
$ω = 4$
$2 = (4 T^{2} \times A \times \frac{1}{2})$
$A = \frac{1}{4}$
$V = ω \times \sqrt{(A)^{2} - x^{2}}$
$x = \frac{A}{2}$
$V = ω A \times \frac{\sqrt{3}}{2}$
$V = 0.866 m / s e c$