Simple harmonic motion amplitude, frequency, period and energy

[Naldo6]

A 424 g mass vibrates according to the equation x=0.342 sin(5.20t) where x is inn meters and t is in seconds. Find the amplitud, frquency, period, total energy, kinetic energy when x=12.0 cm, and potencial nergy when x-12.0 cm.

Amplitud=0.342

w=2*pi*frequency
frequency=(2*pi)/w=(2*pi)/(5.20)=1.208 Hz

Period= 1/frequncy=1/1.208= 0.828

E=1/2*k*x^2
in the amplitud it is
E=(1/2)*(k)(0.342)^2

but k= (w^2)*m=(5.20^2)*(0.424)=11.46

E=(1/2)*(11.46)*(0.342^2)= 0.670 J

Potenicial Energy= 1/2*k*x^2
=(1/2)*(11.46)*(0.12^2)=8.25 x 10^-2 J

Kinetic Energy= Total - Potencial= 0.670 J - 8.25x10^-2 J = 0.5875 J


Is all this problem correct or not?...

 

[thejinx0r]

Everything looks right, assuming no calculation errors.

 

[Naldo6]

ok thanks...