Assume a pendulum, a mass M attached to a massless rod, which is oscillating in small angle. According to the oscillating equation(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\ddot{\theta} + \frac{g}{l}\theta = 0[/tex]

We find that the frequency is proportional to [tex]\sqrt{g/l}[/tex]. Now if the pendulum is accelerated upward at acceleration [tex]a[/tex], since [tex]a[/tex] is along the opposite direction as the gravity [tex]g[/tex], the frequency of the accelerated pendulum should be

[tex]\omega = \sqrt{\frac{g-a}{l}}[/tex]

why in textbook, in said the frequency becomes [tex]\omega = \sqrt{\frac{g+a}{l}}[/tex]?

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# Accelerated pendulum

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