Vibrations

Question 1

Natural frequency =

Answer 1

omega = (k/m)^1/2

Question 2

In forced vibrations the oscillating body vibrates with the

Answer 2

Frequency Of external force

Question 3

Equation for forced vibrations

Answer 3

d2x/dt2 = -kx/m -(b/m)dx/dt + F•coswt/m

Question 4

Amplitude of forced vibrations is

Answer 4

Generally small

Question 5

Motion equation for forced vibrations

Answer 5

Ma = -kx - bv + F•coswt

Question 6

Amplitude of forced vibrations

Answer 6

X = X•sin(wt + phi)

Where
X• = (F•/m)/ ((w•^2 - wd^2)^2 + (bw/m)^2 )^1/2

Question 7

Force in case of damped vibrations

Answer 7

Ff = -bv

Question 8

Amplitude of damped vibrations

Answer 8

Decreases exponentially

Question 9

Energy of damped vibrations

Answer 9

Decreases exponentially

Question 10

Resultant force of damped vibrations

Answer 10

F = Fr + Fd = -kx - bv

Question 11

Energy equation for damped vibrations

Answer 11

E = (1/2) kxm^2 e^(-bt/m)

Question 12

Amplitude equation of damped vibrations

Answer 12

X = Xm e^(-bt/m) sin(wt + phi)

Where w= (w•^2 - (b/2m)^2)^1/2

Question 13

Equation of damped vibrations

Answer 13

d2x/dt2 = -kx/m - (b/m)dx/dt

Question 14

Resonant vibrations

Answer 14

Are a special case of forced vibrations