1. Harmonic Motion (IV) Energy of a simple harmonic oscillator
Physics 1D03 - Lecture 34

2. Energy of a SHO Recall: ETot = K + U = 1/2mv2 + 1/2kx2
for a spring. But we know that: x=A cos(ωt+φ) v=-A ω sin(ωt+φ)
Physics 1D03 - Lecture 34

3. Energy in SHM M Look again at the block & spring Hence: ETot = ½kA2
We could also write E = K+U = ½ m(vmax )2
Physics 1D03 - Lecture 34

4. Suppose you double the amplitude of the motion, what
Concept Quiz
Suppose you double the amplitude of the motion, what
happens to the maximum speed ?
Doubles
4 x Larger
Doesn’t change
Physics 1D03 - Lecture 34

5. Suppose you double the amplitude of the motion, what
Concept Quiz
Suppose you double the amplitude of the motion, what
happens to the maximum acceleration?
Doubles
4 x Larger
Doesn’t change
Physics 1D03 - Lecture 34

6. Suppose you double the amplitude of the motion, what
Concept Quiz
Suppose you double the amplitude of the motion, what
happens to the the total energy?
Doubles
4 x Larger
Doesn’t change
Physics 1D03 - Lecture 34

7. Energy
Since we know the total energy of a SHM, we can calculate the or displacement velocity at any point in time: ETot=1/2kA2 = K+U = 1/2mv2 + 1/2kx2
So, if x=0, all E is in kinetic, and v is at max if x=A, all E is in potential, and v is zero
Physics 1D03 - Lecture 34

8. Example
A 100g block is 5cm from the equilibrium position moving at 1.5m/s.
a) What is the total energy of the system ?
b) What is the amplitude of the oscillations ?
Physics 1D03 - Lecture 34

9. Example A 500g block on a spring is pulled 20cm and released.
The motion has a period of 0.8s. What is the velocity when the block is 15.4cm from the
equilibrium ?
Physics 1D03 - Lecture 34

10. Example
A 1.0kg block is attached to a spring with k=16N/m. While the block is at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 40cm/s.
what is the amplitude of the subsequent oscillations ?
what is the block’s speed at the point where x=A/2 ?
Physics 1D03 - Lecture 34