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## Homework Statement

Is the tension in the string of a pendulum, when averaged over time, larger or smaller than the weight of the pendulum? Quantify your answer. You may also assume that the angular amplitude of the oscillations is small.

## Homework Equations

For tension ##T##, angular displacement of the pendulum ##\phi## and length of the pendulum ##l##

$$T = mgcos(\phi)+ ml\dot{\phi}^2$$

$$\phi = Asin(\omega t)$$

## The Attempt at a Solution

I am lost at the "when averaged over time" part. I think the only way to "quantify" the answer is to examine the value of $$T_{average} - mg$$ But I don't know how to average T.