A block with mass m =6.9 kg is hung from a vertical spring. When the mass hangs

Question

A block with mass m =6.9 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.27 m. While at this equilibrium position, the mass is then given an initial push downward at v = 3.9 m/s. The block oscillates on the spring without friction.

I calculated the spring constant at 251 N/m which is correct.

This gave me an omega of 6.03 sec^-1. (251 N/m/6.9 kg)^(1/2)

I am trying to find the velocity at t=0.35 sec.

When I do my calculations I keep getting -3.4 m/s which it says is incorrect.

Explanation / Answer

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. If this helps then kindly rate 5-stars

A block with mass m =6.9 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.25 m. While at this equilibrium position, the mass is then given an initial push downward at v = 3.8 m/s. The block oscillates on the spring without friction.

1)

What is the spring constant of the spring?

N/m

Your submissions:

Computed value:

270.48

Submitted:

Thursday, April 17 at 10:00 PM

Feedback:

Correct!

2)

What is the oscillation frequency?

Hz

Your submissions:

Computed value:

1

Submitted:

Thursday, April 17 at 10:00 PM

Feedback:

Correct!

3)

After t = 0.33 s what is the speed of the block?

m/s

4)

What is the magnitude of the maximum acceleration of the block?

m/s2

5)

At t = 0.33 s what is the magnitude of the net force on the block?

N

6)

Where is the potential energy of the system the greatest?

At the highest point of the oscillation.

At the new equilibrium position of the oscillation.

At the lowest point of the oscillation.

solution:

1) K = mg/x = (6.9*9.8)/0.25 = 270.48 N/m

2) f = W/2pi = sqrt(K/m)/2pi = ((270.48/6.9)^.5)/(6.28) = 1 Hz

3) 0.5*m*V^2 = 0.5*K*A^2

A = 0.61 m

y = A*sinwt = 0.61*sin6.28t

at t= 0.33

y = 0.61*sin(6.28*0.33) = 0.53486 m

V = dy/dt = W*A*cos(wt) = 6.28*0.61*cos(6.28*0.33) = ?1.84197 m/s

4) a = -W^2*A = -24.05742 m/s^2

5) F = m*a = mW^2*y = 6.9*6.28^2*0.53486 = 145.54876 N

6) At the highest point of the oscillation.

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