- #1
erik-the-red
- 89
- 1
Question:
A frictionless block of mass 2.35 kg is attached to an ideal spring with force constant 310 N/m. At t=0 the spring is neither stretched nor compressed and the block is moving in the negative direction at a speed of 12.6 m/s.
1. Find the amplitude.
I got this without a problem. I used the formula A = square root of [tex]x_i^2[/tex] + [tex]v_i^2[/tex]/[tex]\omega^2[/tex]. [tex]\omega = \sqrt{k/m} = 11.49[/tex] rad/s. Plugging in known values results in 1.10 m, which is correct.
2. Find the phase angle.
Here's where I don't know why my answer is not correct.
I use the equation [tex]v_i = -\omega * A * sin(\omega*t + \phi)[/tex]. I know the initial velocity, I know the angular frequency, and I know the amplitude. I'm solving for the angle in radians.
[tex]-12.6 = -(11.49)(1.10)(sin(\phi)[/tex] This is at time t, so [tex]\omega * t[/tex] = 0.
I get [tex]\phi = 85.5 ^\circ[/tex]. Converting it into radians, it's 1.49 (rad).
This isn't right, though.
A frictionless block of mass 2.35 kg is attached to an ideal spring with force constant 310 N/m. At t=0 the spring is neither stretched nor compressed and the block is moving in the negative direction at a speed of 12.6 m/s.
1. Find the amplitude.
I got this without a problem. I used the formula A = square root of [tex]x_i^2[/tex] + [tex]v_i^2[/tex]/[tex]\omega^2[/tex]. [tex]\omega = \sqrt{k/m} = 11.49[/tex] rad/s. Plugging in known values results in 1.10 m, which is correct.
2. Find the phase angle.
Here's where I don't know why my answer is not correct.
I use the equation [tex]v_i = -\omega * A * sin(\omega*t + \phi)[/tex]. I know the initial velocity, I know the angular frequency, and I know the amplitude. I'm solving for the angle in radians.
[tex]-12.6 = -(11.49)(1.10)(sin(\phi)[/tex] This is at time t, so [tex]\omega * t[/tex] = 0.
I get [tex]\phi = 85.5 ^\circ[/tex]. Converting it into radians, it's 1.49 (rad).
This isn't right, though.
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