Answer to Question #83289 in Classical Mechanics for prince

Question

The total energy of a particle executing simple harmonic motion of period 2\π s is 0.256J. The displacement of the particle at π/4 is 8\sqrt{2} cm. Calculate the mass of the particle.
a. 20 Kg
b. 50 Kg
c. 15 Kg
d. 30 Kg

Answer 1

The displacement of a particle executing sinple harmonic motion

x=x_max sin⁡(2π/T t)=x_max sin⁡(t)

8√2=x_max sin⁡〖π/4=x_max √2/2 〗

x_max=16 cm=0.16 m

Total energy

E=(mω^2 x_max^2)/2=(4π^2 mx_max^2)/(2T^2 )

So, the mass of the particle

m=(ET^2)/(2π^2 x_max^2 )=(0.256×2)/〖0.16〗^2 =20 kg