Thank you When physicists say \"frequency,\" they usually mean the angular frequ
ID: 1282099 • Letter: T
Question
Thank you
When physicists say "frequency," they usually mean the angular frequency omega = 2pi/T, in radians per second. Engineers on the other hand sometimes mean f = 1/T (sometimes also called v) in cycles per second, which is called Hz. The AC in the wall is at 60 Hz. Suppose a SHO has a mass of 20kg and is oscillating at 60 Hz, with an energy of 100J. What is its amplitude? What is its maximum velocity? A force of 100N is applied to a SHO, which stretches it a distance of 0.1 m. Compute the work done, using W = Fdx. When released, the mass m oscillates with a frequency of 5 radians per second. Using energy conservation, determine the mass m. A SHO has m = 1kg and is oscillating with energy 100J. A 1kg ball of putty is dropped straight down from above, on the SHO mass, and it sticks. Find the new energy of the SHO if the putty hits when the spring was maximally stretched. Also, find the energy of the SHO if the putty hits when the spring was at the equilibrium position.Explanation / Answer
x(t) = A*sin(wt+fi)
v(t) = dx/dt = w*A*sin(wt+ fi) =w*x(t) that is v(max) = wA
a(t) =dv/dt = -w^2*x(t), that is a(max) = - w^2*A
a)
w=2*pi*F =2*pi*60
E = mV^2(max)/2 = m(wA)^2/2
A^2 =2E/(m*w^2) = 2*100/20/(2*pi*60)^2 =7.036*10^-5 m^2
A =8.388 mm
V(max) =w*A =(2*p*60)*8.388*10^-3 =3.162 m/s
b)
If the force is constant then
W =F*x =100*0.1 =10 J
W =Emax = mV(max)^2/2 = m(wA)^2/2
m = 2W/(wA)^2 = 2*10/ (5*0.1)^2 = 80 kg
c)
When the spring is at maximum extension all energy is poetential.
Emax= K*X^2/2 and does not depend on oscillator mass.
Thus at maximum extension the energy remains the same.
When the spring is in equilibrium position all energy is kinetic.
E(max) = m*V(max)^2/2
If the mass doubles (mass of putty = mass of oscilator = 1 kg) then the energy doubles.
New energy is double: E(new) =2*E(max) =2*100 =200 J
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.