A block is attached a horizontal spring ( k = 12.4 N/m) exhibits simple harmonic
ID: 1495284 • Letter: A
Question
A block is attached a horizontal spring (k = 12.4 N/m) exhibits simple harmonic motion on a flat, frictionless table.
The mass is observed to have a maximum displacement of 8.50 cm from its equilibrium position and completes 8 cycles in 10 seconds. At time t = 0, the mass is 1.00 cm to the left of equilibrium and is travelling to the left.
Assume the positive direction is to the right.
a) Find the angular frequency of the block.
b) Find the mass of the block.
d) Find the total energy stored in the block at t = 3.0 s
Explanation / Answer
b.)completes 8 cycles in 10 seconds
T = 10/8 = 1.24 sec
T = 2pi sqrt(m/k)
m is mass of block
k is spring constnt
1.24 = 2*pi *sqr(m/12.4)
m =0.482 Kg
a)
w = 2*pi*f
w = 2*pi/T
w = 2*pi/1.24
w= 5.06 rad/sec
w is angular frequency
d.)total energy = 0.5kx^2
TE = 0.5*12.4*0.046^2 = 0.01311 J
c.)-1 = 0.085 Cos(5.06t)
x(t)= 0.085 Cos(5.06t)
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