QUESTION 2 Consider a harmonic oscillator with mass 0.34 kg and spring constant
ID: 1473315 • Letter: Q
Question
QUESTION 2 Consider a harmonic oscillator with mass 0.34 kg and spring constant 199 N/m. If the amplitude is 7.74 cm, what is the speed of the mass at the equilibrium point? (work this out using conservation of energy. Practise how to draw an energy bar chart for this.) Answer with units of m/s.
QUESTION 3 Consider a harmonic oscillator with frequency 5 Hz. If the amplitude of the oscillation is 5.73 cm, what is the speed of the mass at the equilibrium point? (work this out using conservation of energy. Practise how to draw an energy bar chart for this.) Answer with units of m/s.
Explanation / Answer
mass m= 0.34 kg, spring constant k= 199 N/m, amplitude A= 0.0774 m
T.E=P.E@amplitude= 1/2*k*x^2 =1/2*199 *0.0774 ^2=0.596J
at the equilibrium point T.E =K.E
1/2*0.34*v^2 = 0.596J
=>v^2=3.506m/s =>v=1.8725m/s
3))frequency f= 5 Hz, amplitude A= 0.0573 m
w=2*PI*f= 31.416
w=sqrt(k/m) =>k/m =986.96
T.E=1/2*k*x^2 =k*1.6416*10^-3J
at the equilibrium point T.E =K.E
=>1/2*m*v^2=k*1.6416*10^-3J
=>v^2 =2*(k/m)*1.6416*10^-3 =2*(986.96)*1.6416*10^-3=3.2404
=>v=1.8m/s