- #1

happyparticle

- 405

- 20

- Homework Statement
- Finding when the oscillations of the mass A will be at the minimum amplitude for the first time.

At t = 0, pendulum A = ##x_a = 5cm## and pendulum B = ##x_a = 0##

- Relevant Equations
- normal modes coordinates

##q_p(t) = A cos \omega_p t##

##q_b(t) = B cos \omega_b t##

First of all, I found the angular frequencies for both pendulum and breathing mode which are

##\omega_p = 4.95##

##\omega_b = 7.45##

Then I found the normal mode coordinates equations:

##q_p(t) = A cos \omega_p t##

##q_b(t) = B cos \omega_b t##

And the beating frequency (I'm not sure if I need it or even if the value is correct)

##f_{beat} = 0.4##

Because the initial velocities are zero, the amplitude of each normal mode is equal to the initial value of the normal mode coordinate.

The pendulum A is at ##x_a = 5## and because the pendulum B is at ##x_a = 0## the initial position of the pendulum a (I guess)##q_p = x_1 + x_2, q_b = x_1 - x_2##

##q_p = 5 + ?, q_b = 5 - ?##

then

##q_p(t) = (5 + ?) cos \omega_p t##

##q_b(t) = (5-?) cos \omega_b t##

I know as well that

##x_1 = \frac{q_p(t) + q_b(t)}{2}##

##x_2 = \frac{q_p(t) - q_b(t)}{2}##

I'm stuck there. I still not sure about ##x_2## position and I can't see when the oscillations of the pendulum A will be at the minimum amplitude for the first time.

##\omega_p = 4.95##

##\omega_b = 7.45##

Then I found the normal mode coordinates equations:

##q_p(t) = A cos \omega_p t##

##q_b(t) = B cos \omega_b t##

And the beating frequency (I'm not sure if I need it or even if the value is correct)

##f_{beat} = 0.4##

Because the initial velocities are zero, the amplitude of each normal mode is equal to the initial value of the normal mode coordinate.

The pendulum A is at ##x_a = 5## and because the pendulum B is at ##x_a = 0## the initial position of the pendulum a (I guess)##q_p = x_1 + x_2, q_b = x_1 - x_2##

##q_p = 5 + ?, q_b = 5 - ?##

then

##q_p(t) = (5 + ?) cos \omega_p t##

##q_b(t) = (5-?) cos \omega_b t##

I know as well that

##x_1 = \frac{q_p(t) + q_b(t)}{2}##

##x_2 = \frac{q_p(t) - q_b(t)}{2}##

I'm stuck there. I still not sure about ##x_2## position and I can't see when the oscillations of the pendulum A will be at the minimum amplitude for the first time.

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