elasticity and simple harmonic motion?

Question

please help me with this problem

1. the simple pendulum has a mass of 200 grams and length of 2.5 m.What is the period of pendulum?To make the period three times,how long must the pendulum be?

2.The young's modulus of elasticity of aluminum wire is 7x10^10 pa.What force is needed to stretch the wire by 0.002 m if the wire is 0.001 in diameter and 0.60 m long ?Find stress and strain.

3. Wires A and B are made of same material but A has diameter twice that of wire B. If the stress on A is equal to the stree on B,what is the relation between the force on each wire?

please help....dont get this

i really appreciate if you can help me to solve this problem
BIG THANKS ! !

Answer 1

I'll do number 1 for you, someone else can do 2 and 3.

Time Period = 2 * pi * sqrt (length / acceleration due to gravity)

Therefore-:

Time = 2 x pi x sqrt (2.5 / 9.81)

Time = 3.171869925 seconds

You now want a period 3 times this amount i.e. 9.515609774 seconds. (so we re-arrange the equation to find Length)

We now have-:
g T^2 / 4 * pi^2 = Length

9.81 * 9.515609774^2 / 4 * pi^2 = Length

Length = 22.5 metres.

Answer 2

chico! Doctor Q is correct! Mark his answer as the best. Then repost #2 and #3 so that me or others could also answer you.