A 0.39 kg block is attached to an ideal spring of force constant 15N/m executes
ID: 1382985 • Letter: A
Question
A 0.39 kg block is attached to an ideal spring of force constant 15N/m executes simple harmonic motion on a fricitonless horizontal surface. At time t=0s, the block has a displacement of 0.9m.
a. What is the frequency of the oscillations of the cart?
b. Determine the maximum speed of the cart. Where does the maximum speed occur?
c. Find the maximum accleeration of the mass. Where does the maximum accleration occur?
d. How much total energy does this oscillating system contain?
e. Express the displacement as a function of time using a cosine function.
Explanation / Answer
From the given data
Amplitufe of the motion, A = 0.9 m
a) angular frequncy, w = sqrt(k/m)
= sqrt(15/0.39)
= 6.2 rad/s
we know, w = 2*pi*f
==> f = w/(2*pi)
= 6.2/(2*pi)
= 0.9875 Hz
b) Vmax = A*w
= 0.9*6.2
= 5.58 m/s
c) a_max = A*w^2
= 0.9*6.2^2
= 34.6 N
d) Total enrgy = 0.5*k*A^2
= 0.5*15*0.9^2
= 6.075 J
e) x = A*cos(w*t)
x = 0.9*cos(6.2*t)
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