Two SHM are represented by the equations x 1 = 20 sin ⁡ 5 π t + π 4 and x 2 = 10 sin ⁡ 5 π t + 3 cos ⁡ 5 π t . The ratio of the amplitudes of the two motions is

For SHM 1 , x 1 = 20 sin ⁡ 5 π t + π 4 Its amplitude, A 1 = 20 For SHM 2 , x 2 = 10 sin ⁡ 5 π t + 3 cos ⁡ 5 π t = 10 × 2 sin ⁡ 5 π t 2 + 3 2 cos ⁡ 5 π t 20 sin ⁡ 5 π t . cos ⁡ π 3 + sin ⁡ π 3 cos ⁡ 5 π t = 20 sin ⁡ 5 π t + π 3 It's amplitude, A 2 = 20 ∴ A 1 A 2 = 20 20 = 1

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Physics - SHM Question with Solution | TestHub

PhysicsSHMMiscellaneousEasy2 minPYQ_2020

PhysicsEasysingle choice

Two SHM are represented by the equations $x_{1} = 20 \sin [5 π t + \frac{π}{4}]$ and $x_{2} = 10 (\sin 5 π t + \sqrt{3} \cos 5 π t)$ . The ratio of the amplitudes of the two motions is

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Answer:

Solution:

For SHM $(1)$ ,

$x_{1} = 20 \sin (5 π t + \frac{π}{4})$

Its amplitude, $A_{1} = 20$

For SHM $(2),$

$x_{2} = 10 [\sin 5 π t + \sqrt{3} \cos 5 π t]$

$= 10 \times 2 (\frac{\sin 5 π t}{2} + \frac{\sqrt{3}}{2} \cos 5 π t)$

$20 (\sin 5 π t . \cos \frac{π}{3} + \sin \frac{π}{3} \cos 5 π t)$

$= 20 \sin (5 π t + \frac{π}{3})$

It's amplitude, $A_{2} = 20$

$∴ \frac{A_{1}}{A_{2}} = \frac{20}{20} = 1$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:SHMSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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