What is the time period of a pendulum on an inclined plane?

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SUMMARY

The time period of a pendulum suspended from a cart on an inclined plane can be calculated using the formula T = 2π√(l/geff), where geff represents the effective gravitational acceleration. In this scenario, the effective gravity is determined by the component of gravitational force acting perpendicular to the incline. The challenge lies in deriving the effective gravity for various angles of inclination and understanding the dynamics of the pendulum in a non-inertial reference frame.

PREREQUISITES
  • Understanding of pendulum motion and the formula T = 2π√(l/g)
  • Knowledge of effective gravitational force (geff) in inclined systems
  • Familiarity with basic concepts of non-inertial reference frames
  • Ability to apply trigonometric functions to resolve forces
NEXT STEPS
  • Study the derivation of effective gravitational force on inclined planes
  • Learn about the dynamics of pendulums in non-inertial frames
  • Explore advanced pendulum motion equations for varying angles of inclination
  • Investigate the impact of friction and other forces on pendulum behavior
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in the dynamics of pendulums on inclined planes.

Abhishekdas
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Period of a pendulum...

Homework Statement


A simple pendulum of length l is suspended from the ceiling of a cart which is sliding without friction on an inclined plane of inclination theta. What will be the time period of the pendulum?


Homework Equations


T=2(pi) root(l/geff)



The Attempt at a Solution


There is this concept of geff(g effective) which i don't know how to apply...So basically how to do this sum?
 
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when the (pendulum + cart)system moves along the inclined plane, they do not feel the effect of any gravity in that direction as if they were in free fall in the sliding direction.
so, what remains is the g component perpendiculur to the slide direction, which is your effective g in this case.
 


Ya...that is okay...for this sum...but in general how to find the direction of g(eff)...
I mean for some general cases there must be some way to find the time period using the general method ...ie showing that the a=-w^2*x or torque=-w^2(theta) for the system and then using T=2(pi)/w... For other cases i have done it many times...even for a normal pendulum(the commom derivation)...But i am not getting such a method for tilted pendulums...
 

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