The graph shown below indicates the position as a function of times for a mass o

Question

The graph shown below indicates the position as a function of times for a mass of 2 kg oscillating at the end of a borizontal, massless spring The position, x, is measured in meters and the time t is recorded in seconds. (a) what is the amplitude of the motica? (b) what is the frequency of the motion? (c) what is the spring constant of the spring? (d) How long does it take the mass to travel from x = 0 to x = A/2? (e) what is the total mechanical energy of the system? (f) what are the initial position and velocity of the mass? (g) write the quation of motion [x(t) =?] for the mass attached to the spring. (h) write the equation for the velocity as a function of time for the mass.

Explanation / Answer

a)
Amplitude is maximum displacement in position which is 6 m
Answer: 6 m
b)
Time period, T = 0.2 s
f = 1/T
= 1/0.2
= 5 Hz
Answer: 5 Hz
c)
w = sqrt(k/m)
2*pi*f = sqrt (k/m)
2*pi*5 = sqrt (k/2)
k = 1974 N/m
Answer: 1974 N/m
d)
let
x = A*sin (2*pi*f*t)
for x=A/2
A/2 = A*sin (2*pi*f*t)
0.5 = sin (2*pi*f*t)
pi/6 = 2*pi*f*t
t=1/(12*f)
=1/(12*5)
=0.017 s
Answer: 0.017 s

I am allowed to answer only 4 parts at a time. Please ask other as different questions

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.