shm and waves

1. Chapter’s Name: SHM
Lecture No. : 3
Faculty Name: Karmendra Tyagi

2. A particle of mass 2 kg is moving on a straight line under the action
force F = (8 - 2x) N. It is released at rest from x = 6m. (A) Is the
particle moving simple harmonically?
(B)Find the equilibrium position of the particle. (C) Write the equation of
motion of the particle. (D) Find the time period of SHM.

3. SHM AS A PROJECTION OF UNIFORM CIRCULAR MOTION.

4. SHM AS A PROJECTION OF UNIFORM CIRCULAR MOTION.

5. SHM AS A PROJECTION OF UNIFORM CIRCULAR MOTION.
-A +A
+A
-A

6. SHM AS A PROJECTION OF UNIFORM CIRCULAR MOTION.
If the particles cross each other , they are equal
phase away from x axis.
If the particles are at maximum
separation from each other , they are
equal phase away from y axis.

7. Two particles undergo SHM along parallel lines with the same time period (T) and equal
amplitudes. At a particular instant, one particle is at its extreme position while the other is
at its mean position. They move in the same direction. Find the time when they cross each
other.

8. Two particles execute SHM of same amplitude of 20 cm with same period along the same
line about the same equilibrium position. If phase difference is /3 then find out the
maximum distance between these two.

9. Two particles execute SHM of same time period but different amplitudes along the same
line. One starts from mean position having amplitude A and other starts from extreme
position having amplitude 2A. Find out the time when they both will meet?

12. Potential Energy (U) of a body of unit mass moving in a one-dimension
conservative force field is given by, U = (x2 – 4x + 3). All units are in S.I.
(i) Find the equilibrium position of the body.
(ii) Show that oscillations of the body about this equilibrium position is
simple harmonic motion & find its time period.
(iii) Find the amplitude of oscillations if speed of the body at equilibrium
position is 2 6 m/s.

14. ENERGY OF SHM

15. • A particle performing pure SHM does not dissipate energy and
continues to perform similar motion periodically
• Only conservative forces do work during SHM
• Total energy of a particle performing SHM (mechanical energy) remains
constant
ENERGY OF A PARTICLE PERFORMING SHM

16. KINETIC ENERGY
• Max K.E at mean position
• Min K.E at extreme (zero)
• Decreases as we go away from mean position

17. POTENTIAL ENERGY
Let minimum potential energy be Um (at mean position)-

18. THE GRAPHS OF ENERGIES/POSITION
For mean position at origin and minimum potential energy to be zero-
m=0
x
E
x=+A
x=-A
K.E
P.E
T.E
t

19. Potential Energy (U) of a body of mass 2 kg moving in a one-
dimension conservative force field is given by, U = (x2 – 4x + 3).
If total energy of the particle is 8 J determine-
(i) Maximum speed of the particle
(ii) Amplitude of the oscillation
(All units are in S.I.)

20. Ans-d

21. ENERGY/TIME GRAPH-
K.E
t
Kinetic/Potential energy perform SHM of
double frequency/ half time period
P.E
t

22. The average kinetic energy in one-time period in simple harmonic
motion is-
(Assume minimum potential energy to be zero)
(D) Zero

23. A body is executing simple harmonic motion. At a displacement x from mean, its
potential energy is E1 and at a displacement y from mean, its potential energy is
E2. The potential energy E at a displacement (x + y) is-
(Given minimum potential energy is zero)
(A) E1 + E2 (B) (C) E1 + E2 + (D)