A particle executes SHM with amplitudes $25$ cm and period $3$ seconds. The minimum time required for it to move between two points $12.5$ cm on either side of the mean position is
0.75 sec
0.25 sec
0.50 sec
1.00 sec

Question

A particle executes SHM with amplitudes $25$ cm and period $3$ seconds. The minimum time required for it to move between two points $12.5$ cm on either side of the mean position is
0.75 sec
0.25 sec
0.50 sec
1.00 sec

Toppr Admin · Accepted Answer

Asin-x3B8-12-525sin-x3B8-12-5sin-x3B8-12-x3B8-300-x2234-2-x3B8-60Time taken for -xA0-360o is 3 sec-x2234-Time taken for 600 is -3-xD7-60360-0-5-xA0-sec

A particle executes SHM with amplitudes 25 cm and period 3 seconds. The minimum time required for it to move between two points 12.5 cm on either side of the mean position is0.75 sec0.25 sec0.50 sec1.00 sec

Asinθ=12.525sinθ=12.5sinθ=12θ=300∴2θ=60Time taken for 360o is 3 sec∴Time taken for 600 is =3×60360=0.5 sec

A particle executes SHM with amplitudes $25$ cm and period $3$ seconds. The minimum time required for it to move between two points $12.5$ cm on either side of the mean position is
0.75 sec
0.25 sec
0.50 sec
1.00 sec

$A s i n θ = 12.5$
$25 s i n θ = 12.5$
$s i n θ = \frac{1}{2}$
$θ = 30^{0}$
$∴ 2 θ = 60$
Time taken for $360^{o}$ is 3 sec
$∴$ Time taken for $60^{0}$ is $= \frac{3 \times 60}{360} = 0.5 s e c$