Question

The total energy of a partical executing simple harmonic motion of period `2pi` secon is 10,240ert. The displacement of the particle at `pi//4` second is `8sqrt(2)cm`. Calculate the amplitutde of motion and mass of the particle

Answer 1

Here. `T=2pis,E=10,240erg,t=pi//4s, y=8sqrt(2)cm.`
As `y=rsin ((2pi)/(T)t`
`:. 8sqrt(2)=rsin((2pi)/(2pi))xx(pi)/(4)=r sin((pi)/(4))`
or `r=(8sqrt(2))/(sinpi//4)=(8sqrt(2))/(1//sqrt(2))=16cm`
As `E=(2pi^(2)mr^(2))/(T^(2)) or m =(ET^(2))/(2pi^(2)r^(2))`
`:. m =(10,240xx (pi)^(2))/(2pi^(2)xx(16)^(2))=80g. `