Cycloid. A particle moves in the x y -plane. Its coordinates are given as functi

Question

Cycloid. A particle moves in the xy-plane. Its coordinates are given as functions of time by
x(t)=R(tsint)y(t)=R(1cost)
where R and are constants.

Part A

Determine the velocity x-component of the particle at any time t.

Express your answer in terms of some or all of the variables R, and t .

RRcos(t)

Part B

Determine the velocity y-component of the particle at any time t.

Express your answer in terms of some or all of the variables R, and t.

Rsin(t)

Part C

Determine the acceleration x-component of the particle at any time t.

Express your answer in terms of some or all of the variables R, and t .

Rsin(t)

Part D

Determine the acceleration y-component of the particle at any time t.

Express your answer in terms of some or all of the variables R, and t.

Rcos(t)

Part E

At which times is the particle momentarily at rest?

Express your answer in terms of the variables n, , and appropriate constants.

2n

Part F

What is the x-coordinate of the particle at these times?

Express your answer in terms of some or all of the variables R, n, , and appropriate constants.

Part G

What is the y-coordinate of the particle at these times?

Express your answer in terms of some or all of the variables R, n, , and appropriate constants.

Part G

What is the y-coordinate of the particle at these times?

Express your answer in terms of some or all of the variables R, n, , and appropriate constants.

Ive done most of the problem im just having trouble with part f, g, and h.

RRcos(t)

Explanation / Answer

given that x(t)=R(tsint) y(t)=R(1cost)

part (A)

velocity at x component is dx/dt= d(R(tsint))/dt

=R-Rcost

part (B)

velocity of y component is dy/dt=d(R(1cost) )/dt

=Rsint

part (C)

acceleration of x component is d^2x/dt^2=d(R-Rcost)/dt

=Rsint

part (D)

acceleration of y component is d^2y/dt^2=d(Rsint)/dt

=Rcost

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.