Solving Two Wave Problems: Angular Frequency & Pendulum Periods

[Jacob87411]

1) A 2KG block hangs without vibrating at the end of a spring (k = 500 N/m) that is rising with an upward acceleration of G/3 when the acceleration suddenly ceases (at t=0). (A) What is the angular frequency of oscillation of the block after the acceleration ceases? (B) By what amount is the spring stretched during the time that the elevator car is accelerating?

Is part A just asking how long it takes the block to go from its maximum compressed spot to its most stretched spot and back? And I'm having a hard time figuring out B, just where to start.

2) A light balloon filled with helium of density .18 kg/m^3 is tied to a light string of length L = 3meters. The string is tied to the ground forming an inverted pendulum. If the balloon is displaced slightly from equilibrium, it undergoes simple harmonic motion. Determine the period. Take the density of air to be 1.29 KG / M^3.

Well the period of a pendulum is...

T=2(3.14) multiplied by the square root of mass/(weight/length)

Is this the correct equation to use and if so what should go into weight?

 

[Jacob87411]

Also, I am guessing that the equation for #2 needs to be tweeked a bit because it doesn't seem to take into account the density, unless that goes in for the weight

 

[Pyrrhus]

For the second problem you need to prove

$$\ddot{x} + \omega^2 x = 0$$

Remember the forces acting on the balloon, the buoyant force and the weight.

 

[Jacob87411]

Well if the balloon is inverted its weight is what's pulling it down?

Buoyant force = Density of the object * Gravity * Volume. Without a volume I don't see how it is helpful...I know through Archimedes that the buoyant force on something immersed in a fluid (the air in this case) is equal to the weight of the fluid displaced by that object. Still kind of lost as you can see

By the way, what's the X with two dots over it?

 

[Pyrrhus]

Yes its weight, and aceleration.

 

[Jacob87411]

I'm just not seeing where to go with it all, i have missed awhile in class so i may be missing something, been looking through the text.

The density of the object is going to effect its acceleration..The period is obviously going to be effected by the length of the string which is 3 M. Its downward motion is caused by its weight and acceleration, just don't see how to put it all together, and what would cause the pendulum system to swing back up once it got down to one end


Side note for anyone else reading; figured out the first problem so don't need help on that one