What is the Period and Amplitude of a Pendulum on a Rocket?

[iwonde]

Homework Statement

A rocket is accelerating upward at 4.00 m/s^2 from the launchpad on the earth. Inside a small 1.50-kg ball hangs from the ceiling by a light 1.10-m wire. If the ball is displaced 8.50 degrees from the vertical and released, find the amplitude and period of the resulting swings of the pendulum.

Homework Equations

T = 2pi \sqrt{L/g}
\omega = /sqrt{g/L}
x = Acos(\omegat + \phi)

The Attempt at a Solution

I think this is a simple pendulum problem.

T = 2pi /sqrt{1.1/4} = 3.29 s, I relplaced g with the upward acceleration of the rocket.

I'm trying to solve for A from the equation that I have for x, but I don't have t.

 

[DavidWhitbeck]

**** About acceleration *****

You identified the wrong acceleration. The pendulum would fall at a rate of g if the rocket was unaccelerated, right? Your procedure would indicate otherwise. You would formally argue this from Newton's 2nd Law, but I'll just tell you that you should replace g with a + g. That way (a) if a = 0 you get back what you usually have, and (b) if a = -g the rocket is in freefall, the pendulum does not work and you get an infinite period.

**** About amplitude *****

Don't look at that equation, think about what is happening physically. Amplitude is the maximum displacement of whatever is executing periodic motion. In the case of the pendulum, it is the angular displacement that is executing periodic motion and it can go no further than it's initial displacement of 8.50 degrees because if it is dropped from rest, it's the turning point of the motion, going out further in angular displacement from the vertical would require negative kinetic energy, which is impossible.

 

[Gear300]

The ball on the pendulum is feeling Earth's gravitational force and a force due to a noninertial system. Sum up the two accelerations. If it is assumed the net acceleration is constant, then the amplitude of the pendulum should stay approximately constant. The amplitude is the farthest angle the pendulum will travel from the equilibrium point, which in this case is the initial displacement. The amplitude for a pendulum is given in radians...so the answer for that should just be the conversion of 8.50 degrees to radians. The period of the pendulum depends on the acceleration, which in this case is the net acceleration. Using that and the length of the wire, you could find the period.