# Platform on Springs: Find Effective Spring Constant & Oscillation Amplitude

• confused1
In summary, a platform of mass 0.8 kg is supported by four springs and a chunk of modeling clay with mass 0.6 kg is dropped onto it with a speed of 0.9 m/s. The clay sticks to the table and the table and clay oscillate together until the table comes to rest 6 cm below its original position. The effective spring constant of all four springs together can be found by calculating the net displacement and force required to compress the springs. Additionally, a conservation of momentum can be used to determine the velocity of the clay/platform combination immediately after collision.
confused1
A platform of mass 0.8 kg is supported on four springs (only two springs are shown in the picture, but there are four altogether). A chunk of modeling clay of mass 0.6 kg is held above the table and dropped so that it hits the table with a speed of v = 0.9 m/s.

The clay sticks to the table so that the the table and clay oscillate up and down together. Finally, the table comes to rest 6 cm below its original position.

a) What is the effective spring constant of all four springs taken together?

b) With what amplitude does the platform oscillate immediately after the clay hits the platform?

Can you show us what work and/or ideas you have put forth so far?

a) What is the net displacement Delta x of the spring from its former equilibrium position? What force F was required to compress the springs? The effective spring constant is the ratio F/(delta x).

The first thing in this problem is a conservtion of momentum. Assume the collision is instantaneous, so there are no net forces to worry about. What will be the velocity of the clay/platform combination immediately after collision?

## 1. What is a platform on springs?

A platform on springs is a physical setup consisting of a platform or tray attached to one or more springs. The platform can be used to hold objects or perform experiments, while the springs provide a way to measure and control the movement and oscillations of the platform.

## 2. How do you find the effective spring constant of a platform on springs?

The effective spring constant of a platform on springs can be found by applying a known force to the platform and measuring the resulting displacement. The spring constant can then be calculated using the formula k = F/x, where k is the spring constant, F is the applied force, and x is the displacement.

## 3. What factors affect the spring constant of a platform on springs?

The spring constant of a platform on springs can be affected by various factors such as the type and material of the springs, the number of springs used, the placement of the springs, and the weight and distribution of the load on the platform.

## 4. How do you determine the oscillation amplitude of a platform on springs?

The oscillation amplitude of a platform on springs can be determined by measuring the maximum displacement of the platform from its equilibrium position during one complete oscillation. This can be done by using a ruler or a motion sensor.

## 5. What are the applications of a platform on springs?

A platform on springs has various applications in physics and engineering, such as studying simple harmonic motion, testing the strength and elasticity of different materials, and designing and testing suspension systems for vehicles. It can also be used in education and demonstrations to visualize and understand concepts related to oscillations and springs.

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