The motion of a particle varies with time according to the relation $y = a sin$ $ω$ $t + a cos$ $ω t$ . Then
the motion is oscillatory but not SHM
the motion is SHM with amplitude $\frac{a}{2}$
the motion is SHM with amplitude $a$
the motion is SHM with amplitude $a$ $\sqrt{2}$

Question

The motion of a particle varies with time according to the relation $y = a sin$ $ω$ $t + a cos$ $ω t$ . Then
the motion is oscillatory but not SHM
the motion is SHM with amplitude $\frac{a}{2}$
the motion is SHM with amplitude $a$
the motion is SHM with amplitude $a$ $\sqrt{2}$

Toppr Admin · Accepted Answer

Y-a-xA0-sin-xA0-x3C9-t-a-xA0-cos-xA0-x3C9-t-a-x221A-2sin-x3C9-t-R4-Clearly amplitude is a-x221A-2 and motion is SHM-because a-d2ydt2-x2212-a-x221A-2-x3C9-2sin-x3C9-t-R4-So- a is proportion to -x3C9-2 -which is the condition of SHM-

The motion of a particle varies with time according to the relation y=asinωt+acosωt . Thenthe motion is oscillatory but not SHMthe motion is SHM with amplitude a2the motion is SHM with amplitude athe motion is SHM with amplitude a √2

y=a sin ωt+a cos ωt=a√2sin(ωt+R4)Clearly amplitude is a√2 and motion is SHM.because a=d2ydt2=−a√2ω2sin(ωt+R4)So, a is proportion to ω2 ,which is the condition of SHM.

The motion of a particle varies with time according to the relation $y = a sin$ $ω$ $t + a cos$ $ω t$ . Then
the motion is oscillatory but not SHM
the motion is SHM with amplitude $\frac{a}{2}$
the motion is SHM with amplitude $a$
the motion is SHM with amplitude $a$ $\sqrt{2}$

$y = a s i n ω t + a c o s ω t$
$= a \sqrt{2} s i n (ω t + \frac{R}{4})$
Clearly amplitude is $a \sqrt{2}$ and motion is SHM.
because $a = \frac{d^{2} y}{d t^{2}} = - a \sqrt{2} ω^{2} s i n (ω t + \frac{R}{4})$
So, $a$ is proportion to $ω^{2}$ ,which is the condition of SHM.