CE$6102$E STRUCTURAL DYNAMICS CE$6102$E STRUCTURAL DYNAMICS

Tutorial Sheet $1$

A rigid block of mass $M$ is suspended from a uniform pulley of mass $m$ and radius $R$ as shown in Fig$\mathrm{.}1.$

If the cord is inextensible, of negligible weight, and does not slip on the pulley, and the spring stiffness

is $k,$ determine the equation of motion for vertical vibration of the system.

Figure $1$

Obtain the equation of motion for small vibrations of the system shown in Fig$\mathrm{.}2.$

A harmonic motion has an amplitude of $0\mathrm{.}2$ cm and a period of $0\mathrm{.}15$ s $.$ Determine the maximum

velocity and acceleration.

A harmonic motion has a frequency of $10$ cps and its maximum velocity is $4\mathrm{.}57\frac{m}{s}.$ Determine its

amplitude, period and its maximum acceleration.

Design an arrangement of three springs with stiffness $40,60$ and $90\frac{N}{m}m,$ respectively to have an

effective stiffness of $76\frac{N}{m}m.$

Write the equation of motion for the system shown in Figure $3.$

A uniform bar of length $L$ and weight $W$ is suspended symmetrically by two strings, as shown in

Fig$\mathrm{.}4.$ Set up the differential equation of motion for small angular oscillations of the bar about the

vertical axis $O-O,$ and determine its period.

For the rigid beam shown in Fig$\mathrm{.}5,$ obtain the equation of motion and determine the

generalized quantities $m^{*},c^{*},k^{*}$ and $f^{*}(t).$ Total mass of the beam is $M.$

Tutorial Sheet $1$

A rigid block of mass $M$ is suspended from a uniform pulley of mass $m$ and radius $R$ as shown in Fig$\mathrm{.}1.$

If the cord is inextensible, of negligible weight, and does not slip on the pulley, and the spring stiffness

is $k,$ determine the equation of motion for vertical vibration of the system.

Figure $1$