Please explain step by step! thank you. 1)A harmonic oscillator consisting of an
ID: 1296519 • Letter: P
Question
Please explain step by step! thank you.
1)A harmonic oscillator consisting of an ideal spring attached to a mass has a period of 1.6 s. The oscillator is displaced from the equilibrium position by 2 cm and then released. What is the speed of the mass when it has returned half the distance to the equilibrium position?
2)A harmonic oscillator consisting of an ideal spring attached to a mass has a period of 1.1 s. The oscillator is displaced from the equilibrium position by 2.6 cm and then released. What is the speed of the mass when it has returned half the distance to the equilibrium position?
Explanation / Answer
1)T =2*pie *(m/k)^0.5 = 1.6
m/k = 0.064
w= 3.92 rad/sec
0.5*k*0.02*0.02 = 0.5*k*0.01*0.01 + 0.5*m*v*v
v = 0.0684 m/s
2)T = 2??(m/k)
1.1 = 2*3.14*?(m/k)
m/k = 0.175
m = 0.175*k
Total energy = 1/2*ka^2 = 1/2*k*0.026^2
When half way from equilibrium position, Total energy = KE + PE = 1/2*mv^2 + 1/2*kx^2
= 1/2*mv^2 + 1/2*k*(a/2)^2
= 1/2*m*v^2 + 1/2*k*0.026^2/4
Energy conservation: 1/2*k*0.026^2 = 1/2*m*v^2 + 1/2*k*0.026^2/4
Or, 1/2*mv^2 = 1/2*k*(3/4)*0.026^2
1/2*(0.175*k)v^2 = 1/2*k*(3/4)*0.026^2
v = 0.0538 m/s