Solving Pendulum Confusion: m*a=-k*x Explained

[LLT71]

I find it somehow confusing to imagine why m*a=-k*x is "generally valid". that minus sign bothers me. Imagine I raised a bob to some height (ex. from the left side) and then released it. from that moment till the moment where it reaches equilibrium position m*a and restoring force have same direction. from a moment where it "goes of" the equilibrium position to the moment when it reaches the same height on the right side m*a and restoring force have different direction and so on. should it be m*a=+-k*x? what I'm missing?

 

[BvU]

$ma$ IS the restoring force. The direction is opposite from the displacement from equilibrium

 

[LLT71]

$ma$ IS the restoring force. The direction is opposite from the displacement from equilibrium

god I feel so stupid... thanks that was straight forward!

 

[BvU]

No need to feel stupid. It looked convincing ! And: you are welcome.

 

[mpresic]

for a pendulum with small amplitude: the equation of motion is approximately: mass* length^2 *angular acceleration = - mass * gravitational acceleration * length * angle.

the k does not come in. the restoring torque is - mass * gravitational acceleration * length * angle. The magnitude of the restoring force is: mass * gravitational acceleration. The - sign come in because the gravitational acceleration is always downward, and acts to close the angle theta. if the bob is on the left hand side, for example theta is less than zero and the force acts to increase theta. If the bob is on the right hand side, theta is greater than zero, and the gravitational force acts to decrease theta. the gravitational force always acts against the angular displacement theta.