Contents [show]
A single point with mass m is vibrating harmonically. The displacement x from point of balance is governed by the differential equation
where ω is a positive constant.
b) What is the speed, the acceleration, and the force at the mass as a function of time t and constants A, B.
Solution
The derivative of x(t)=A sinωt+B cos ωt
is the speed u(t)=x'(t)=Aω cosωt-B ωsinωt
And the derivative of speed is the acceleration
a(t)=u'(t)=x''(t)=-〖ω^2 Α sin〗ωt-ω^2 B cosωt
The force at the mass is
A single point with mass m is vibrating harmonically. The displacement x from point of balance is go...
The problem: Determine the cross-sectional area and the position of the centroid for the sectio...
The problem: Determine the second moments of area, Ixx and Iyy, for the sections indicated in...
Calculate the equation of the elastic curve .Determine the pinned beam’s maximum deflection. EI cons...
Calculate the distance x for locating roller support so that the moment on the beam at point B is ze...
Calculate the member diagrams. Solution We have already calculated the external beam rea...
Calculate the reactions and member forces. Solution We calculate the reactions. Section 1 0...
Calculate the reactions and member forces. Solution We calculate the reactions. ...
Find the maximum moment of the above beam which is subjected to triangular vertical load. SOLUTION:...