SHM

Question 1

Differential equations in SHM?

Answer 1

F=-kx
a=F/m=-(k/m)x=-ω^ x
Slope= -k
ω=ω=√k/m

Question 2

What is the necessary condition for a period motion to be SHM?

Answer 2

Force f must be directly proportional to the negative of x

Question 3

General solution of Simple harmonic motion ?

Answer 3

x= A sin(ωt±δ)
here , x is displacement from mean position. A is amplitude , δ is phase angle and ωt±δ is phase angle at a general time t.

Question 4

If x= A sin ωt, then what is v and a?

Answer 4

v= ωA cos ωt
a=-ω² A sin ωt.
Phase difference between x-t and v-t fiction is π÷2 but phase difference between x-t and a-t function is π.

Question 5

What is velocity v at a general point in SHM?

Answer 5

v=ω√Α²−x²

it’s max at mean position(=ωA) and min at extreme position(=0)

Question 6

In SHM what is formula for acceleration a?

Answer 6

a=-ω²x

it’s min (=0) at mean position and max (=-ω²A) at extreme position.

Question 7

In SHM, what is formula of potential energy PE?

Answer 7

PE= U₀+½kx²

Question 8

In SHM what is the formula for kinetic energy?

Answer 8

KE= ½ k(A²−x²)

Question 9

In SHM what is the formula for total energy TE?

Answer 9

TE= U₀+½ kA²= U₀ + mω²Α².

Question 10

When is potential energy minimum and maximum in SHM?

Answer 10

Potential energy is minimum at mean position and maximum at extreme position.

Question 11

When is kinetic energy minimum and maximum in SHM?

Answer 11

Kinetic energy is maximum at mean position and zero at extreme position.

Question 12

What is U vs x or KE vs x graph like ?

Answer 12

The graph is a parabola.