A 0.60-kg object is attached to one end of a spring, as in the first drawing, an
ID: 1775208 • Letter: A
Question
A 0.60-kg object is attached to one end of a spring, as in the first drawing, and the system is set into simple harmonic motion. The displacement x of the object as a function of time is shown in the second drawing. With the aid of these data, determine (a) the amplitude A of the motion, (b) the angular frequency , (c) the spring constant k, (d) the speed of the object at t = 1.0 s, and (e) the magnitude of the object's acceleration at t = 1.0 s.
ti Displacement Time 33320 Pen Amplitude =A Amplitude = A x=0mis the equilibrium position of the object x (m) 0.080 0 0.080 4.0 0 3.0 Time (s) 1.0Explanation / Answer
a)
From the graph the distance of the particle in the wave movesbetween ± 0.080m
So the maximum distance is amplitude is A=0.080m
b)
From the diagram period of the motion T = 4 s
The angular frequency = 2/T
= 2(3.14)/4 s
= 1.57 rad/s
c)
The period of the spring mass system is
T = 2pi square root (m/k)
4 s = 2(3.14) square root(0.60 kg/k)
k = 1.48 N/m
d)
At t = 1.0 s, mass is at the maximum displacement from the equilibrium
Therefore spaad of the mass at t = 1 s is zero.
e)
The wave represents a sine wave
Let y = A sin(t) be the equation of the wave,
Then the acceleration is
a = d2y/dt2
a = -2y
the acceleration at t = 1.0 s
a = -2A (at t = 1.0 s , y = A)
a = -(1.57 rad/s)^2(0.08 m)
a = -0.197 m/s^2
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.