# Find the period of the resulting swings of this pendulum

## Homework Statement

A rocket is accelerating upward at 3.70 m/s^2 from the launchpad on the earth. Inside a small 1.50-Kg ball hangs from the ceiling by a light 1.10m wire.

a)If the ball is displaced 8.50 degrees from the vertical and released, find the amplitude of the resulting swings of this pendulum

b)If the ball is displaced 8.50 degrees from the vertical and released, find the period of the resulting swings of this pendulum

x=A(coswt+θ)
-mgθ=-mgx/L
θL=x
w=sqrt(g/L)
T=2pi sqrt(g/L)

## The Attempt at a Solution

the new g' of the rocket is g-arocket=9.8-3.7=6.1 m/s^2
θL=x 0.1484*1.1=0.16324m
w=sqrt(g/L)=sqrt(6.1/1.1)=2.3549
x=A(coswt+θ)
A=x/cos(wt+θ) now taking t for 0 (this is probably the part where I made my mistake)
A=0.16324/cos(0+0.1484)=0.1148 for the amplitude

b)
T=2pi sqrt(g/L)
T=2pi sqrt(6.1/1.1)=2.67s

In both cases my answers are wrong, if anyone could give me a pointer I would appreciate the help.

the formula for the period is wrong, it should be

T=2*pi*sqrt(L/g)

As for the acceleration, what would it feel like if you were launched in the space shuttle, would you feel lighter or heavier as the rocket was accelerating upwards? In other words how does the acceleration of the rocket combine with the acceleration by gravity?

ah thats were I went wrong, Okay I now figured out b but I'm still having difficulty with part a. I'm not sure what to use for my t value.