Figure below shows a body of mass m attached to a spring of stiffness k. Find the differential equation for the displacement, x Show that x=Acos(wt)+Bsin(wt) where A, B are constants and w= √k/m

Problem 2: A student pushes a baseball of m = 0.18 kg down onto the top of a vertical spring that has its lower end fixed to a table, compressing the spring a distance of d = 0.14 meters from its equilibrium length. The spring constant of the spring is k = 740 N/m. Let the gravitational potential energy be zero at the position of the baseball in the compressed spring. Randomized Variables m = 0.18 kg k = 740 N/m d = 0.14 m

Jum The mass of the block depicted in the image is 1.60 kg. The spring has a spring constant of 76.9 N/m. The coefficient of static friction between the block and the floor is 0.726. Assume that the spring makes no contact with the floor and therefore friction only acts on the block. How far must the block and spring assembly be compressed to just barely overcome the force of static friction acting on the block? Report your result in meters.

The graph shows the measured force for a spring as it is compressed through various displacements.

A 25.0 cm long spring is hung vertically from a ceiling and stretches to 30.5 cm when a 6.50 kg mass is hung from its free end. HINT (a) Find the spring constant (in N/m). N/m (b) Find the length of the spring (in cm) if the 6.50 kg weight is replaced with a 165 N weight. cm

I need help solving the equations symbolically and I don't know how to get the m value for the first part.

Three forces act on a statue. Force F⃗ 1F→1 (magnitude 45.0 NN) points in the +x-direction, Force F⃗ 2F→2 (magnitude 105 NN) points in the +y-direction, and force F⃗ 3F→3 (magnitude 235 NN) is at an angle of 36.9∘∘ from the -x-direction and 53.1∘∘ from the +y-direction. counterclockwise from the +x-direction. Find the x- and y-components of the net external force F⃗ F→ on the statue. Find the magnitude and direction of the net external force exerted on the statue.

Two blocks of masses m, = 4.0 kg and mg = 8.0 kg are connected with a string that passes over a very light pulley (Figure 1). Friction in the pulley can be ignored. Block 1 is resting on a rough table and block 2 is hanging over the edge. The coefficient of friction between the block 1 and the table is 0.70 (assume static and kinetic friction have the same value). Block 1 is also connected to a spring with a constant 300 N/m. In the initial state, the spring is relaxed as a person is holding block 2, but the string is still taut. When block 2 is released, it moves down for a distanced until it stops (the final state). Figure 1 of 1

An engineer is designing a spring to be placed at the bottom of an elevator shaft. If the elevator cable should break when the elevator is at a height of 103m above the top of the spring, calculate the value that the spring stiffness constant should have so that passengers undergo an acceleration of no more than 3.9g when brought to rest. Let 924kg be the total mass of the elevator and passengers.

The tension in a ligament in the human knee is approximately proportional to the extension of the ligament, if the extension is not too large. If a particular ligament has an effective spring constant of 152 N/mm as it is stretched, what is the tension in this ligament when it is stretched by 0.800 cm?