If natural frequency ω of the system shown in figure is x 5 m k , find x.

If the hanging mass moves x, the mass on the incline moves 2x and its speed is 2v. Energy: TE = 2 1 m v 2 + 2 1 m ( 2 v ) 2 + 2 1 k ( 2 x ) 2 = 2 5 m v 2 + 2 k x 2 . ω = 5 m 4 k = 2 5 m k ⇒ x = 2 . Answer: 2.

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PhysicsSHMCalculation of time periodMedium2 minQB

PhysicsMediuminteger

If natural frequency $ω$ of the system shown in figure is $x \frac{k}{5 m}$ , find x.

Answer:

Solution:

If the hanging mass moves x, the mass on the incline moves 2x and its speed is 2v. Energy:

$TE = \frac{1}{2} m v^{2} + \frac{1}{2} m (2 v)^{2} + \frac{1}{2} k (2 x)^{2} = \frac{5}{2} m v^{2} + 2 k x^{2}$ .

$ω = \frac{4 k}{5 m} = 2 \frac{k}{5 m} \Rightarrow x = 2$ . Answer: 2.

Stream:JEESubject:PhysicsTopic:SHMSubtopic:Calculation of time period

⏱ 2mℹ️ Source: QB

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