Using Matlab to solve dynamics problem

[spin360]

I've attached my problem set. I'm having an issue on how to write the formula to insert it into matlab. According to the problem set, dl/dt = 0.2m/s. I actually have the "solution" to the problem, though I don't understand why the answer is what it is. Basically, my instructor used the pythagorean theorem and set l$$^{2}$$ = b$$^{2}$$ + $$^{2}$$. He then differentiated twice w.r.t time, hence dc/dt going to 0 (c is constant) and the second derivative of dl/dt going to 0 as well (dl/dt constant). The end result is d$$^{2}$$b/dt$$^{2}$$ = (dl/dt)$$^{2}$$ - (db/dt)$$^{2}$$. a (acceleration) is the second deriv of b evidently. Can anyone tell me the reason behind differentiating twice, also how I could possibly use that formula in matlab? Thanks.

 

[Aaron Bex]

Your instructor used the Pythagorean theorem because he was trying to find the acceleration of the particle, which is the second derivative of position. The equation he wrote is a differential equation that can be used to find the acceleration by solving for db/dt^2. In Matlab, you can use either the ode45() or dsolve() commands to solve the differential equation and find the acceleration.

 

[oswaler]

I understand your confusion about the solution to your dynamics problem. Let me try to break it down for you in a way that will hopefully make more sense.

First, let's look at the formula that your instructor used: l^{2} = b^{2} + ^{2}. This is a representation of the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (l) is equal to the sum of the squares of the other two sides (b and ^).

Next, your instructor differentiated this formula twice with respect to time (t). This is because your problem involves dynamics, which is the study of how objects move and change over time. By differentiating twice, your instructor is essentially finding the acceleration (a) of the object, which is the second derivative of the position (b) with respect to time.

Now, let's look at the resulting formula: d^{2}b/dt^{2} = (dl/dt)^{2} - (db/dt)^{2}. This formula represents the acceleration (a) of the object, which is equal to the square of the velocity (dl/dt) minus the square of the acceleration (db/dt). This is a common formula used in dynamics problems to find the acceleration of an object.

To use this formula in Matlab, you will need to define the variables (l, b, and ^) and their initial values. Then, you can use the "diff" function to differentiate the formula twice with respect to time. Finally, you can plug in the values for the velocity (dl/dt) and acceleration (db/dt) to solve for the acceleration (a).

I hope this explanation helps you understand the reasoning behind your instructor's solution and how to use the formula in Matlab. Good luck with your problem set!