Spring Oscillation: Find Greatest Speed of 0.5kg Block

[Leviticus 08]

Homework Statement

A 0.5 kg block attached to an ideal spring (k = 100 N/m) oscillates on a horizontal frictionless surface. When the spring is 12 cm shorter than its equilibrium length, the speed of the block is 1.5 m/s. What is the greatest speed of the block?

Homework Equations

The force becomes F(x) = m a - k x
The equilibrium position is x = m a / k

I don't know what else to use

The Attempt at a Solution

I don't really have all the work at my fingertips I left it at home(I'm at work now)
I'm not looking for a solid solution just somewhere to start

 

[rl.bhat]

The velocity of the block is given by
v =sqrt(k/m)*sqrt(A^2 - x^2) where x is the displacement from the equilibrium position.
Substitute the values and find the A.
For maximum velocity x = ...?

 

[tomcue]

I would approach this problem by first understanding the concept of spring oscillation and its mathematical representation. From the given information, we can determine that the block has a mass of 0.5 kg and is attached to a spring with a spring constant of 100 N/m.

Next, we can use the equation F(x) = m*a - k*x to determine the force acting on the block at a given position x. In this case, the equilibrium position is x = m*a/k. From the given information, we know that the spring is 12 cm shorter than its equilibrium length, so we can calculate the force at this position.

Using the equation F(x) = m*a - k*x and plugging in the known values, we can solve for the acceleration of the block. This acceleration will be constant throughout the oscillation.

To find the greatest speed of the block, we need to consider the conservation of energy in the system. At the equilibrium position, the block has potential energy stored in the spring. As it moves away from the equilibrium position, this potential energy is converted into kinetic energy. At the maximum displacement, the block will have the maximum kinetic energy, which corresponds to the greatest speed.

We can use the equation for kinetic energy (KE = 1/2 * m * v^2) to calculate the maximum speed of the block. Plugging in the known values, we can solve for the maximum speed of the block.

In summary, to find the greatest speed of the block, we need to use the equations for force, acceleration, and energy conservation in the spring-block system. By considering the known values and using these equations, we can calculate the maximum speed of the block.