A simple harmonic oscillator consists of a block of mass 0.2kg at the end of a s

Question

A simple harmonic oscillator consists of a block of mass 0.2kg at the end of a spring of sti?ness 100 N/m.

The spring is observed to have a displacement of x(t = 0) = 0.2 m and an x-component of velocity vx(t = 0) = ?5m/s

at time t = 0.

A) What are the angular frequency (in rad/s), frequency (in Hz), and period of the resulting motion?

B) What is the total energy of the oscillator.

C) Find the amplitude of the motion using energy considerations.

D) Find the maximum speed that the mass has during its motion. Use energy considerations.

Explanation / Answer

A) W = sqrt(k/m) = (100/0.2)^.5 = 22.36 s^-1

B)
E = 0.5*K*x^2 + 0.5*m*V^2 = (0.5*100*0.2^2) + (0.5*0.2*5^2)= 4.5 J

C) E = 0.5*k*A^2

A = 0.3 m

D) E = 0.5*m*Vmax^2

Vmax = 6.71 m/s

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