# Mechanism behind a simple pendulum [closed]

Show that the tension in a simple pendulum is of the form $$T(t)= T_0 + T_2 \cos(\omega t)$$ and find $$T_0$$ and $$T_2$$ in terms of the mass $$m$$ of the bob, the amplitude of the oscillation $$θ_0$$ and acceleration due to gravity, $$g$$.

I understand how to resolve the forces and have the correct answer, but I do not know why it is correct. I resolved such that:

$$T-mg\cos\theta = \frac{mv^2}l$$ and worked from there to get the answer. But why is this resolving correct? Isn't the centripetal acceleration in a perpendicular direction to the components I resolved?

## closed as off-topic by John Rennie, Thomas Fritsch, eranreches, GiorgioP, glSJun 10 at 16:15

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• When you resolved the components of the forces, did you chose the radial component? That is the component perpendicular to the velocity. Why would you want to be perpendicular to the velocity-based perpendicular component? I think you confused yourself by going one step too far. – Bill N Jun 8 at 12:57