# 5 TF Oscillations (2)

```Energy in the SHO
If the mass is at the limits of its mo-on,
the energy is all poten-al.
If the mass is at the equilibrium
point, the energy is all kine-c.
Again there is only poten-al energy at the
turning points:
When the mass is in between the turning
point and the equilibrium:
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Energy in the SHO
The total energy is constant!
Poten-al energy func-on of a spring:
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Lecture Exercise
A 4 kg block on a fric-onless table is aCached to a horizontal spring with
k=400 N/m. The spring is ini-ally compressed with 5 cm.
-5cm
a) Find the work done on the block by the spring as the block moves from
x= x1 = -5 cm to its equilibrium posi-on x2 = 0 cm
b) Determine the func-on x(t) of the block
c) Determine the func-on v(t) of the block
e) Determine the accelera-on a(t) of the block
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Lecture Exercise Solution
A 4 kg block on a fric-onless table is aCached to a horizontal spring with
k=400 N/m. The spring is ini-ally compressed with 5 cm.
a) Find the work done on the block by the spring as the block moves
from x= x1 = -5 cm to its equilibrium posi-on x2 = 0 cm
19
Lecture Exercise Solution
A 4 kg block on a fric-onless table is aCached to a horizontal spring with k=400 N/
m. The spring is ini-ally compressed with 5 cm.
b) Determine the speed v(t) of the block at x2
20
Lecture Exercise
A 4 kg block on a fric-onless table is aCached to a horizontal spring with
k=400 N/m. The spring is ini-ally compressed with 5 cm.
c) Determine the func-on x(t) of the block
21
Lecture Exercise
A 4 kg block on a fric-onless table is aCached to a horizontal spring with
k=400 N/m. The spring is ini-ally compressed with 5 cm.
c) Determine the func-on v(t) of the block
22
Lecture Exercise
A 4 kg block on a fric-onless table is aCached to a horizontal spring with
k=400 N/m. The spring is ini-ally compressed with 5 cm.
d) Determine the func-on a(t) of the block
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