1. Consider two pendulums, 1 and 2, with the same string length L, but with different bob masses m1 and m2. They are coupled by a spring of spring constant k, which is attached to the bobs. Find their equations of motion, for small oscillations, solve for the modes and find their frequencies and configurations.

A particle of mass m attached to a rigid support by a support of constant k. At equilibrium, the spring hangs vertically. This mass-spring system is joined by another identical oscillator, whose spring is hung from the previous mass. Consider only the vertical movement. a)  write the equations of motion of the coupled system b)Compute the normal mode frequencies for one-dimensional vertical oscillations and then show that the ratio of the two normal frequencies is √5+1/√5−1 c)Find the ratio of the amplitudes of the two masses in each separate mode. (You do not need to consider the force of gravity acting on the masses because it is independent of the displacements.)

For given mass (m=10kg) and two springs systems k1=30 N/m and k2= 20N/m. Find the following  1. Circular Frequency and natural frequency  2. If initial displacement is 50 mm and initial velocity is 0, what is max displacement and max velocity.  3

Figure Q3(b) shows a uniform bar AB of mass = 8 kg hinged at point C.Point A is connected to a spring to maintain the bar in vertical direction, and the stiffness k = 500 N/m. If point A is displaced counter-clockwise by a small angle θ = 3.5 degree and released, With the free body diagram and kinetic diagram, determine the initialhorizontal displacement of A. Then determine the period of vibration, the maximum velocity and acceleration at point A.   p.s. This question was previously answered but because the solution images were unable to view I need to re-ask this question