- #1
idir93
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Hello guys i was trying to solve some problem of simple harmonic motion.
as it is well explaind in the title I'm not getting the same result as my textbook manual solution.
Problem:
A block of unknown mass is attached to a spring with a spring constant of 6:50 N/m and undergoes simple harmonic motion with an amplitude of 10:0 cm. When the block is halfway between its equilibrium position and the end point, its speed is measured to be 30:0 cm/s. Calculate (a) the mass of the block, (b) the period of the motion, and (c) the maximum acceleration of the block.
Textbook solution:
(a) Conserving energy
E =1/2kA² = 32:5 mJ
E =1/2k(A/2)²+12mv2 = E/4+1/2mv²
m =(2/v²)(3/4)E =3E/(2v²) = 542 g
My attempt with SHM equation :
x(t) = Asin(ωt + ∅) and ω=[itex]\sqrt{}(k/m)[/itex]
x(t) = Asin(ωt + ∅)= A/2
sin(ωt + ∅) = 1/2 → ωt + ∅ = ∏/6 → t = (∏/6 - ∅)/ω
We have as well: v(t)=dx/dt= Aωcos(ωt + ∅)
And at x=A/2 → v(t)=0.3 m/s
Substituting t in v(t) we'll have Aωcos(∏/6) = 0.3 → after computation done and substituting the value of A and k i find another number different from 542 g.
Am I wrong? Surely yes, but where? Thanks in advance for helping me :)
as it is well explaind in the title I'm not getting the same result as my textbook manual solution.
Problem:
A block of unknown mass is attached to a spring with a spring constant of 6:50 N/m and undergoes simple harmonic motion with an amplitude of 10:0 cm. When the block is halfway between its equilibrium position and the end point, its speed is measured to be 30:0 cm/s. Calculate (a) the mass of the block, (b) the period of the motion, and (c) the maximum acceleration of the block.
Textbook solution:
(a) Conserving energy
E =1/2kA² = 32:5 mJ
E =1/2k(A/2)²+12mv2 = E/4+1/2mv²
m =(2/v²)(3/4)E =3E/(2v²) = 542 g
My attempt with SHM equation :
x(t) = Asin(ωt + ∅) and ω=[itex]\sqrt{}(k/m)[/itex]
x(t) = Asin(ωt + ∅)= A/2
sin(ωt + ∅) = 1/2 → ωt + ∅ = ∏/6 → t = (∏/6 - ∅)/ω
We have as well: v(t)=dx/dt= Aωcos(ωt + ∅)
And at x=A/2 → v(t)=0.3 m/s
Substituting t in v(t) we'll have Aωcos(∏/6) = 0.3 → after computation done and substituting the value of A and k i find another number different from 542 g.
Am I wrong? Surely yes, but where? Thanks in advance for helping me :)