1. A machine component of mass 0.77 kg moves with SHM in a straight line and completes 175 oscillations per minute. Find the accelerating force when the component is 50 mm from mid-travel.

3- The single-degree-of-freedom "manipulator" shown below has total mass m = 1, with the center of mass at and has inertia tensor Rot ¹Pc: Ch= 100 020 002 'd From rest at t = 0, the joint angle 01 moves in accordance with the time function: 0₁ (t) = bt + ct² in radians. Give the angular acceleration of the link and the linear acceleration of the center of mass in terms of frame {1} as a function of t.

When spinning at 500 rotations per minute two washing machines produce two sinusoidal forces with same maximum amplitude of 400N, but their maximum amplitudes are separated in time by 0.0125s. The two machines are placed side by side and to check their effect on a suspended laundry floor it is necessary to find their resultant vertical force. Find time-varying function describing the resultant of the two vertical forces including the amplitude and phase shift relative to one of the two excitation forces.

can you show the steps taken to equation of motion, how do you find the steady displacement of the mass m,find  the total reponse in detail  and the show the step taken to find the force transmitted in the part c.

Prob. 2: An undamped system vibrates with a frequency of 20 Hz and amplitude of 1 mm. Calculate the maximum amplitude of the system's velocity and acceleration.

Do with in minutes

For the problem related to Fundamental.4, a sketch of the considered system showing and naming (or numbering) every part of the system considered, the respective velocity and acceleration of each, and the frame of reference considered is mandatory. Its absence will automatically make the problem false. Gear A on the drive shaft of the outboard motor has a radius rÃ=8 in. and the meshed pinion gear B on the propeller shaft has a radius r=50 in. The point P is located on the propeller's tip at a distance 10 in. from the neutral axis of the propeller's shaft. B At the beginning of the propulsion, the drive shaft rotates with an angular acceleration a = what must be the value of A to have, while starting from rest, vp=28 in.s¹ in 8 seconds ? A. t2.3 rad.s2 where t is in seconds.

Find the periodic-time (T) of a simple pendulum if its natural frequency ( and length is 2 m. Reg No = 007

P=47 T= 0.69 s

Problem 2 Consider the blodk of mass m, connected to a spring of spring constant k and placed on a inclined plane of angle a. Let l be the length of the spring at equili brium, and a be the elongation. The block oscillates and at the same time is rotating around origin O, in the plane of the inclined, by a variable angular velocity . 1. Calculate the degrees of freedom of the block 2. What is the kinetic energy of the block 3. What is the potential energy of the block 4. Write the Lagrangian function (don't derive the Euler Lagrange equa tions) reference plane