# 1. (Non-dimensionalizing the linear pendulum equationConsider the linear pendulum equation:e(0)= 00, de /dt (0) = 2oLdt2(a.) Find the simplest possible combination of L and g that yieldsdimension (sec)-1. Connbing L to getunitsSec(b.) Let Tnew differential equation governing the linearized pendulum using thedimensionless time variable T. Also find the new initial conditions. HowV9/L t. Carry out this change of variables to find themany parameter groupings are there now in the initial value problem?(c.) Let 0* = 0/00. Starting from the initial value problem obtained inpart (b.), carry out this change of variables to obtain another new initialvalue problem governing the linearized pendulum. Update both thedifferential equation and the initial conditions. How many parametergroupings are there now in the initial value problem?(d.) Solve the initial value problem that you obtained in part (c.). Youranswer will be in terms of 0* and T.(e.) As a check on your work, take your answer from part (d.) andrewrite it in terms of the original variables 0 and t. Check that thisresult satisfies the original initial conditions listed before part (a.).

Question
Asked Oct 23, 2019
13 views

pleas ehelp me answer these questions.

a,b,c,d,and e.

thank you!

check_circle

## Expert Answer

Step 1

(a) Write the dimension of L and g

Thus,

The simplest combination of L and g that yields units of (sec)-1 is (g/L)-1/2.

Step 2

(b) Use substitution of variable in the given equation

Step 3

The new boundary conditions for ...

### Want to see the full answer?

See Solution

#### Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in