First slide

Simple hormonic motion

Question

A cylindrical piston of mass M slides smoothly inside a long cylinder closed at one end, enclosing a certain mass of gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position, it oscillates simple
harmonically. The period of oscillation will be

Difficult

A

$T=2π \sqrt{(\frac{Mh}{PA})}$
B

$T = 2 π \sqrt{(\frac{MA}{Ph})}$
C

$T = 2 π \sqrt{(\frac{M}{PAh})}$
D

$T = 2 π \sqrt{(MPhA)}$

Solution

$VΔP + PΔV = 0 or ΔP = P (ΔV / V) or \frac{F}{A} = - P (\frac{Ax}{Ah}) = - P (\frac{x}{h}) F = - P (\frac{Ax}{h}) a = - P (\frac{Ax}{h}) \frac{1}{M} = - (\frac{PA}{Mh}) x thise gives ω^{2} = \frac{PA}{Mh} or T = \frac{2 π}{ω} = 2 π \sqrt{(\frac{Mh}{PA})}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App