# Answer to Question #83289 in Classical Mechanics for prince

Question #83289

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

a. 20 Kg

b. 50 Kg

c. 15 Kg

d. 30 Kg

Expert's answer

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

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