Math Physics Problems Calculus, Calculus Physics Problems?

First of all, it's constantly changing, but how it's changing, you don't know. So you should be less told about the condition that the change from o to 2 is uniformly increased, then there is such a relation:

2t, then when the angle is , =2 t

So v=ds d =a = (gcos)2 t, then: ds d = (gcos)4 t 2 2

So the integral gives s=(4gt 2 2) (cos )d

then t= [s2 (4g (cos)d )].

Since cos d = (1 2) (cos2 +1) d = (-sin2 2+ ) 2

So (cos )d = (-sin2 2+ ) 2- [sin2 2+ ) 2]d

-sin2θ/2+θ)/2-(cos2θ/4+θ^2/2)/2

then t= {4s [g(2+)

The estimation is more complicated, I hope you can understand it...

It can be seen that this is the most valuable question.

First, s is the derivative of t, ds dt=at, and a is brought into the above equation, and we can see that ds dt is everover 0. Therefore, the function s is a monotonic function. Obviously, the maximum and minimum values are taken at the endpoint.

From this we know that when =0, s(0)= gt; When = 2, s( 2) = 0. In this case, s' is the difference between the two, i.e., s' = gt. It can be seen that t' = 2s' g under the root number.

In this way, it is good to replace the acceleration a in the equation with the acceleration g of gravity. Sort of solved the problem.

The calculus physics problem given by the subject is actually based on the acceleration a, and the velocity v and displacement x are calculated. Mathematically, it's the problem of finding integrals, ie.

v=∫adt，x=∫vdt

According to the above method, the solution process is given, and attention should be paid to the calculation of complex numbers in the integration process.

It's really a definite integral problem.

This is the calculation of the definite integral, using Newton's Leibniz formula, (a,b)f(x)dx=f(b)-f(a), where f(x) is a primitive function of the function f(x).

Hello, it is a great pleasure to have your question here. Here are some of my thoughts on this issue, and if there are any mistakes, please feel free to point them out. Question 7: The method that was given to you that day was the right one.

Take the full differentiation on both sides of the equation and then replace dp and dv with δp and δv, is the result different from the answer?

Question 8. kinetic energy

ek=∫(x0->x) f(x)dx= -u(x)|(x0->x)=u(x0)-u(x)

potential energy

ep=u(x)

So, total energy

e=ek+ep=u(x0)-u(x)+u(x)=u(x0)

u(x0) is the potential energy at the starting position of m.

In principle, this topic is not difficult, but for you, I am afraid it does not mean much. Because whether it is a competition or a college entrance examination, it will not be examined. If you insist on knowing how to do it, you will be able to satisfy your curiosity and desire for knowledge. Then you just look down.

A is subjected to F and elastic force, and B is subjected to elastic force. Let the displacement of a be x1 and the displacement of b be x2, then the elastic force is k(x1-x2). So:

f-k(x1-x2)=mx1''

k(x1-x2)=mx2''

Add the two formulas, and you want to subtract to get:

f=mx1''+mx2''=m(x1+x2)''

m（x1-x2）''+2（x1-x2）-f=0

Let x1+x2=x; x1-x2=y.Gotta :

f=mx‘’

my''+2y-f=0 ②

For Immediately we can find: x=(1 2)(f m)t 2+at+b; a, b are constants.

For , which is a non-homogeneous linear differential equation, you need to find the homogeneous solution of the homogeneous linear differential equation and the special solution of the non-homogeneous linear differential equation. Obviously, the special solution is y=f 2; The corresponding homogeneous linear differential equation is:

my''+2y=0

His characteristic equation is: mr 2+2=0

The solution is a complex solution: r1 = root number (2 m) i, r2 = - root number (2 m) i, i is an imaginary number unit. Let r = root number (2 m).

So the solution of the homogeneous equation is: y=c1*cosrx+c2*sinrx, c1, c2 are constants.

The conditions brought into the initial state can be specifically calculated. No more details.

There's a lot of stuff involved, and you may know a little bit about calculus, but you're afraid you don't know about differential equations, and you don't know about differential equations. Also, you may not have learned about imaginary numbers. Imaginary equations, you shouldn't be very good either.

So, you don't need to know how to do it.

Stupid The most basic force analysis and calculus operations.

Hehe, the problem of dynamics, my head is big.

I had to bai

Assuming it is a circular orbit, DU would not be able to analyze it. Give a zhi idea, but I can't solve the micro dao equation. Inside.

The first thing to do is to determine the speed.

The tolerance is large enough or small enough to be either large enough to achieve a full circular motion (velocity at the highest point is not less than (gr)) or small enough that the highest point of motion is not higher than the center of the circle.

mv0 2=mv0 2+mgr(1-cos) is the central angle of the ball from its lowest point to the center of the circle.

v=ωr=rdθ/dt

Obtain (d dt) = (v0 r) + 2g(1-cos) r to solve the differential equation to get the relation to t.

For cases where the velocity is small enough, the maximum height that the ball can reach can be calculated according to the conservation of mechanical energy, so that the maximum value of can be known.

I think there are two scenarios.

1.When 1 2mv mgr, the ball can only shake in the bottom half. It's a time.

2.When the above equation is , the ball can go around the circle smoothly, which is another world.

For the calculation of the specific time, points are used.

Elliptic integrals can only be calculated by computer, and there is no unified formula.

What does Newton's second law say? --f=ma and f=-kv - ma=-kv and a=dv dt - mdv dt=-kv, the above expression is logical. The physical meaning is also clear!

What is the physical meaning of your use of mda=-kdv? How do I get this expression? Is this necessary?