Tricky spring problem. Amplitudes and AccelerationMax

In summary, a 6.7 kg block is hung from a vertical spring and given an initial push downward at 4.7 m/s. After 0.4 seconds, the speed of the block is calculated using the amplitude, stretched distance, k, and mass. The magnitude of the maximum acceleration of the block can be found using the formula aMax = omega^2*t. The amplitude is found to be 0.7655 and the oscillation frequency is 0.9771168341. To find the speed at any given point, the formula sqrt(k/m) * sqrt(amplitude^2 - stretched or compressed distance^2) can be used. Alternatively, the speed can also be calculated using the equation
  • #1
yigh
2
0

Homework Statement



A block with mass m =6.7 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.26 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.7 m/s. The block oscillates on the spring without friction.

3)After t = 0.4 s what is the speed of the block?
4)What is the magnitude of the maximum acceleration of the block?

Calculated K = 252.5384615
Oscillation Frequency (omega) = .9771168341

Homework Equations



Amplitude = vMax*sqrt(m/k)



The Attempt at a Solution


I got amplitude to be 0.7655.
I used -(omega)*Acos(omega*t) to find V for number 3. I used aMax = omega^2*t
 
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  • #2
I believe there is an equation that you use to find the velocity at any given point given amplitude, stretched distance, k and mass. hold on... so its the sqrt(k/m) times the sqrt(amplitude^2 - stretched or compressed distance^2) use that
 
  • #3
oh nevemind. use 9.8m/s^2(t) to find the speed after sometime. isn't the acceleration the same?
 

What is the tricky spring problem?

The tricky spring problem refers to a physics question that involves determining the maximum amplitude and acceleration of a spring in motion. This problem is often used to test understanding of concepts such as Hooke's law and simple harmonic motion.

What is amplitude in relation to a spring?

Amplitude is a measure of the maximum displacement of a spring from its equilibrium position. In other words, it is the distance from the center of the spring to the point where it is stretched or compressed the most. Amplitude is typically represented by the letter A in equations.

How do I calculate the maximum amplitude of a spring?

To calculate the maximum amplitude of a spring, you will need to know the spring constant (k) and the mass (m) attached to the spring. The formula for maximum amplitude is A = (m/k)^1/2, where the units of k are N/m and the units of m are kg. Plug in the values for k and m and solve for A.

What is acceleration in relation to a spring?

Acceleration is a measure of the rate of change of velocity of a spring. In other words, it is the change in velocity per unit of time. Acceleration is typically represented by the letter a in equations and its units are m/s^2.

How do I calculate the maximum acceleration of a spring?

To calculate the maximum acceleration of a spring, you will need to know the spring constant (k) and the maximum amplitude (A). The formula for maximum acceleration is a = (k/m)*A, where the units of k are N/m and the units of A are m. Plug in the values for k and A and solve for a.

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