I know its three problems but they all kind of go together. thanks for the help
ID: 2133196 • Letter: I
Question
I know its three problems but they all kind of go together. thanks for the help in advance.
1.) A simple harmonic oscillator consists of a 150g mass attached to a spring whose force constant is 10^4dy/cm. The mass displaced by 2.5 cm and released from from rest. Calculate a) the natural frequency Vo and the period To. b) the total energy and the maximum speed.
2.) allow the motion in the preceding problem to take the place in a resisting medium, after oscillating for 8s, the maximum amplitude decreases to half the initial value. Calculate a) the damping parameter(calling it B), b) the frequency V1 and compare it with the undamped frequency c) and the decrement of the motion.
3) The oscillator in problem 1 is set in to the motion by giving it an initial velocity 2 cm/s at its equilibrium position. calculate a) the maximum displacement and b) the maximum potential energy.
Explanation / Answer
1) m = 0.15 kg
k = 0.1/0.01 = 10 N/m
x = 0.025m
w = sqrt(k/m) = sqrt(10/0.15) = 8.16 rad/s
f = w/2*pi = 1.3 Hz
T = 1/f = 0.77 s
b) U = 0.5*k*x^2 = 0.003125 J = 3.125*10^-3 J
0.5*m*v^2 = U
v = sqrt(2*U/m) = 0.204 m/s
3)
a) 0.5*k*A^2 = 0.5*m*v^2
A = sqrt(m*v^2/k) = = 0.00245 m = 2.45*10^-3 m = 2.45 mm
b) Umax = Kmax = 0.5*m*v^2 = 0.45*10^-6 J