Please help. Thank you!! A 200g mass attached to a horizontal spring oscillates
ID: 1589576 • Letter: P
Question
Please help. Thank you!!
A 200g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz and an amplitude of 5.0 cm. The mass is pulled 2.5 cm to the right and given an initial velocity of 54.41 cm/s to the right.
(Switch your calculator to radian mode if you use any Cos or Sin functions for this part.)
Determine the following.
A. The angular frequency.
B. The phase constant.
C. The period.
D. The spring constant.
E. The maximum speed and maximum acceleration.
F. The total energy.
G. Write the equation of motion for
position x(t), velocity v(t) and acceleration a(t)(2)
H. Draw a position time graph. (x (t) vs t)
I. Draw a velocity-time graph. (v (t) vs t)
J. Draw an acceleration-time graph. (v (t) vs t)
K. Write the equation of potential energy vs time. Plot the graph.
L. Write the equation of kinetic energy vs time. Plot the graph.
M. Answer the following questions: How many times during a cycle
1. Is the mass at an extreme position?
2. Does the mass have a maximum positive velocity?
3. Does the mass have a maximum speed?
4. Does the mass have a maximum potential energy?
5. Does the mass have a maximum kinetic energy?
Explanation / Answer
A) angular frequency, w = 2*pi*f
= 2*pi*2
= 12.57 rad/s
B) phase constanr, phi = cos^-1(2.5/5)
= 1.047 rad
C) T = 1/f
= 1/2
= 0.5 s
D) we know, w = sqrt(k/m)
w^2 = k/m
==> k = m*w^2
= 0.2*12.57^2
= 31.6 N/m
E) Vmax = A*w
= 5*12.57
= 62.85 cm/s or 0.6285 m/s
F) The total energy = 0.5*k*A^2
= 0.5*31.6*0.05^2
= 0.0395 J