Consider a vertical spring-and-mass system that will be made to oscillate in sim
ID: 2118901 • Letter: C
Question
Consider a vertical spring-and-mass system that will be made to oscillate in simple harmonic motion. The mass is 0.250 kg. Initially, the spring is suspended by itself, unstretched. Then, the mass is attached to the end of the spring, and the spring stretches by 0.45 m, to reach equilibrium. To begin the motion, someone pulls the mass down an additional 0.10 meters, then releases it. (Neglect the effects of air resistance.)
(a.) Is there ever a time during the motion when both acceleration and velocity are equal to zero? Explain.
(b.) Calculate the speed of the mass when it reaches equilibrium again.
(c.) How long will it take the system to oscillate through 5 complete cycles?
(d.) When the mass has maximum velocity, does it also experience a maximum net force? Explain.
Explanation / Answer
a) No there will be no time because it is SHM and it is not possible in SHM
b) w=sqrt(k/m)
kx=mg
k/m = 9.8/0.45
w=sqrt(9.8/0.45) = 4.67
v = wA = 4.67*0.10 = 0.467m/s
c) t = 5*T = 5*2*3.14/4.67 = 6.72 seconds
d) When mass as max velocity it has Net force = 0 , because thats the condition for maximum velocity for any particle