The 3.90 kg cube in the figure has edge lengths d = 5.50 cm and is mounted on an axle through its center. A spring (k = 1150 N/m) connects the cube's upper corner to a rigid wall. Initially the spring is at its rest length. If the cube is rotated 4.00° and released, what is the period of the resulting SHM?

A 20 kg weight is attached to a spring with constant k = 320 kg/m and subjected to an external force F(t) = 1200 cos(2t). The weight begins at rest in its equilibrium position. Find its displacement for t> 0, with y(t) measured positive upwards. y(t) =

3. A rectangular plate of sides 30 cm by 60 cm and a mass m = 2k is suspended from a pin located at the midpoint of one side as shown in the figure. Determine the Period of Vibration. b = 60 cm 30 cm

The 20-lb rectangular plate has a natural period of vibration t = 0.4 s, as it oscillates AB. Neglect the mass of the rod. Suppose that a = 2 ft, around the axis of rod b= 4 ft. (Figure 1) Figure k b 1 of 1 Part A Determine the torsional stiffness k of the rod, measured in lb. ft/rad. Express your answer in pound-feet per radian to three significant figures. ΑΣΦ ↓↑ vec k = Submit U Provide Feedback Request Answer ? lb ft/rad

A spring connects mass m of a pendulum to a wall as shown in the figure. The original un- stretched length of the spring is L. Use the Energy Method and find the equation of motion of the system in terms of the angle 0. L L K m Original Length = L

Two massless springs with different spring constants k₁= 100 N/m and k₂ = 10 N/m are aligned vertically, as shown in figure 1. A block of mass m = 0.12 kg is placed on the bottom spring. The distance between the top of the box and the top spring is h = 0.35 m. You compress the bottom spring Ay = 0.3 m from its equilibrium position (figure 2). When you let go, the box flies up (figure 3) and compresses the top spring (figure 4). Treat the upward direction (↑) as positive, such that the compression of the top spring is a positive displacement. What is the maximum compression of the top spring due to the flying box? Give your answer in units of meters to 2 decimal places. Use g = 9.8 m/s^2. Assume air resistance is negligible. T h EW Ay (2) www Backup link to image (opens in new tab). fumand M риту 4 ² ↑ M ? www

Question 7 A tool machine with mass m = 1000 kg and moment of mass inertia Jo = 300 kg/m² is supported on elastic supports, as shown in the figure. If the stiffness of the supports are given by k₁ = 4000 N/mm and k₂ = 3000 N/mm, and the supports are located at l1 = 0,4 m and 12 = 0,7 m, determine the natural frequencies and modal shapes of the machine tool. 000 -- m, Jo 12- ell 8k₂

A steel ring was shrunk into the outside of a hollow steel disc. The interference radius of the assembly is 40 mm whilst its outer and inner radii are 250 mm and 20 mm, respectively. If the angular speed at which the ring-disc assembly becomes loose is 401.8 rad/sec, determine the shrink-fit pressure at the mating surface of the assembly? Assume that Poisson's ratio for steel is 0.3 and its density is 7860 kg/m³.

only handwritten answer please

The first figure gives spring force Fx versus position x for the spring-block arrangement of the second figure. The scale is set by Fs = 190 N. We release the block at x = 13.0 cm. How much work does the spring do on the block when the block moves from x; = +9.0 cm to (a) x = +5.0 cm, (b) x = -5.0 cm, (c) x = -9.0 cm, and (d) x = -11.0 cm? -x (cm) -2 -1 -F, X* = 0 Block attached to spring F = 0 (a) x positive F, negative F (b) x negative F, positive (c)