Simple harmonic motion in a rocket?

In summary, if the rocket ship is near the Earth in a uniform gravitational field, the period of a pendulum will decrease.
  • #1
PhysicsPhun
55
0
A simple pendulum suspended in a rocket ship has a period T0. Assume that the rocket ship is near the Earth in a uniform gravitational field. (If A and E are true, and the others are not, enter TFFFT).

A) If the ship accelerates upward, the period decreases.
B) If the ship goes into freefall, accelerating downward at 9.81 m/s2, the pendulum will no longer oscillate.
C) If the ship moves upward with a constant velocity, the period decreases.
D) If the mass of the pendulum doubles, the period increases.
E) If the length of the pendulum is doubled, the new period will be the square root of two times T0.

I thought I had the answer on this one. But I didn't..

My instinct was
A)F
B)F
C)T
D)F
E)T

I also tried, TTTFT, TFTFT and FTTFT (ABCDE)

As you can see I was very confident that C=T D=F E=T.. And I was wrong.

Anyone have a better idea?
 
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  • #2
So what i think now is XXFFT

Really not sure on the first two, but i think that C=F D=F E=T
 
  • #3
I'm most probably wrong but I think the answer is given to you at the beginning there.
So far I've come up with TFFFT.
When the ship accelerates upwards won't that increase the value of the downward acceleration due to gravity? So according to the equation
T=sqrt(l/g) (basic equation) wouldn't it cause the period to decrease.
And with the last one I'm think I'm sure (haha) that it is right because if you do the maths it works out as square root of 2 times T0.
I'm pretty sure that the second one is false.
The third one is false as well I think, because if velocity is constant then acceleration is 0. So nothing will happen to the period.
As for D, increasing the mass would decrease the period most likely.
Hope that helps you ;)
 
  • #4
K...you guys...remember this equation for the period of a pendulum when solving...

T = 2(pi) * (length/g) ^ (1/2)...that means that when...

g increases...the period decreases...
...accelerating upwards means that g will be increased on the ship...moving upwards at a constant velocity has NO EFFECT whatsoever on g...I believe that the correct answers are...
A. T (Yes...accelerating upwards will increase g...thus decreases T)
B. T (yes...SHM requires a restoring forces...if the pedulum is in free fall...there is NO restoring force...)
C. F (no...when it is moving at a constant velocity...the value of g is not affected)
D. F (no..the mass of a pendulum as no effect on its period...as you can see from the equation)
E. T (yes...the equation proves this to be the case)
 
  • #5
Cool thanks for the info on the restoring force man ;)
 
  • #6
Thanks a lot for the explanations, you were right on :)
 
  • #7
np man...anytime :-)
 

1. What is simple harmonic motion in a rocket?

Simple harmonic motion in a rocket refers to the periodic back-and-forth motion of a rocket as it moves through the air. This motion is caused by the rocket's propulsion system and is similar to the up-and-down motion of a pendulum.

2. What factors affect the amplitude of simple harmonic motion in a rocket?

The amplitude of simple harmonic motion in a rocket is affected by the force of the rocket's propulsion, the weight and design of the rocket, and the air resistance it encounters. These factors can cause the amplitude to increase or decrease during flight.

3. How does the period of simple harmonic motion in a rocket change during flight?

The period, or the time it takes for the rocket to complete one full cycle of motion, remains constant during flight as long as the rocket's propulsion and design remain consistent. However, external factors such as air resistance can cause slight variations in the period.

4. What is the relationship between simple harmonic motion and the stability of a rocket?

The stability of a rocket is closely related to its simple harmonic motion. A well-designed rocket will have a stable and consistent motion, whereas an unstable rocket may experience erratic or unpredictable motion. This is why engineers carefully consider simple harmonic motion when designing rockets for space exploration.

5. How does simple harmonic motion affect the trajectory of a rocket?

The trajectory, or path, of a rocket is influenced by simple harmonic motion. The back-and-forth motion of the rocket can cause slight deviations in its trajectory, which must be accounted for in its design and navigation. However, with careful planning and control, simple harmonic motion can also be used to stabilize and guide the rocket towards its intended destination.

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