-->

Mechanical Properties Of Fluids

Question
CBSEENPH11020220

A body describes simple harmonic motion with amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is (a) 5 cm, (b) 3 cm, (c) 0 cm.

Solution
Given, 
r
 = 5 cm = 0.05 m
T = 0.2 s
ω = 2π/T = 2π/0.2 = 10 π rad/s
When displacement is y, then acceleration, A = -ω2 y
Velocity, 
 straight v space equals space straight omega space square root of straight r squared minus straight y squared end root

Case space left parenthesis straight a right parenthesis

When space straight y space equals space 5 space cm space equals space 0.05 space straight m space

straight A space equals space minus space left parenthesis 10 space straight pi right parenthesis squared space straight x space 0.05 space

space space space space equals space minus space 5 space straight pi squared space straight m divided by straight s squared space

straight V space equals space 10 straight pi space square root of left parenthesis 0.05 right parenthesis squared space minus space left parenthesis 0.05 right parenthesis squared end root

space space space space space equals space 0

Case space left parenthesis straight b right parenthesis colon

When space straight y space equals space 3 space cm space equals space 0.03 space straight m space

space space space space straight A space equals space left parenthesis negative 10 space straight pi right parenthesis squared space straight x space 0.03 space

space space space space space space space equals space minus space 3 space straight pi squared space straight m divided by straight s squared space

space straight V space equals space 10 straight pi space straight x space square root of left parenthesis 0.05 right parenthesis squared space minus space left parenthesis 0.03 right parenthesis squared end root space

space space space space space space equals space 10 space straight pi space straight x space 0.04

space space space space space space equals space 0.4 space straight pi space straight m divided by straight s

Case space left parenthesis straight c right parenthesis colon

When space straight y space equals space 0

straight A space equals space minus space left parenthesis 10 straight pi right parenthesis squared thin space straight x space 0 space equals space 0

straight V space equals space 10 straight pi space straight x space square root of left parenthesis 0.05 right parenthesis squared minus left parenthesis 0 right parenthesis squared end root space

space space space space equals space 10 space straight pi space straight x space 0.05 space

space space space space equals space 0.5 space straight pi space straight m divided by straight s