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Chapter 8: Q13P (page 436)

The exact equation of motion of a simple pendulum isd2胃/dt2=-蝇2sin鈦�胃where蝇2=g/l. By method (c) above, integrate this equation once to findd胃/dtifd胃/dt=0when胃=90掳. Write a formula fort(胃)as an integral. See Problem 5.34.

Short Answer

Expert verified

The solution of the given differential equation ist(胃)=鈭�l2g鈰�sec鈦�胃d胃+c

Step by step solution

01

Given information

The given equation.

d2胃dt2=-蝇2sin鈦�胃

02

Differential equation

Definition: A differential equation is an equation that relates one or more unknown functions and their derivatives.

03

Solve for differential equation

Equation isd2胃dt2=-蝇2sin鈦�胃

Multiply both side of the equation by d胃/dt

Solve further,


It is given that d胃dt=0at胃=90掳.

So,

0=2蝇2cos鈦�90掳+2c0=0+2cc=0

Thus,

04

Integrate above equation

Integrate both sides,

Therefore, the solution of the given differential equation is t(胃)=鈭�lg鈰�sec鈦�胃d胃+c

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