IIT JEE , AIEEE Forum - Physics , Mechanics

kislay

pls solve

master_purav

Whenever you find two oscillating bodies oscillating about same spring, then use the concept of reduced mass.

reduced mass = m1m2/(m1 + m2)

Here reduced mass = Mm/(M + m)

So,

Time Period:

T = 2 pi Sqrt (m/k)

Here put reduced mass instead of m

Similarly calculate amplitude.

kislay

yaar i know d concept of reduced mass ,but i want to know how it has been derived,that's why posted this question,................
waise i hav rated u 4 ur sincere effort .......

pls let me abt its derivation if u know it............

krishna.gopal

Suppose we are watching the motion in center of mass reference frame.

Let amplitude of mass be a.

By the the time mass m moves by a distance a The car will move a distance of

a' such that

am=a'M

and a+a'=xo

So a = Mxo/(M+m)

When the mass is displaced from its mean position by distance a restoring force of kxo acts on it

So F=-kxo= -(k(M+m)/M)a

So frequency of oscilation

f = (1/2pi)*sqrt((k(M+m)/M)/m)

=(1/2pi)*sqrt(k*(M+m)/(M*m))

And time period = 1/f

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