Question

the period of oscillation of a simple pendulum of length l suspended from the roof of the vehicle which moves without friction down an incline plane of inclination Alpha is given?

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Answer 1

we know that

Bob of the pendulum with respect to the accelerating frame of reference is as follows

F(net) = mgcos@

or net acceleration of the bob is

g(eff) =gcos@

We know that

time period of string

T = 2π √L/√g(eff)

so

T = 2π√L/√gcos@

whenever point of suspension is accelerating

take

T = 2π√L/√g(eff)

g(eff) = g*a

where

a = acceleration of point of suspension

where as

according to question

a = gsin@(down the inclination plane)

so

|g - a| = g(eff) = sqft(g^2 + (gsin@)^2 + 2gsin@cos(90-@))

g(eff) = gcos@

:-)

Answer 2

Answer:

see the attachment......