Calculating Speed of Mass Oscillating on Spring

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Homework Help Overview

The problem involves calculating the speed of a mass oscillating on a spring, described by a position function x(t) = (14.5cm)cos[(14.0s-1)t]. The original poster attempts to find the speed at a specific time, t = 0.820 s, using the relationship between position and velocity in harmonic motion.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the original poster's calculations and question the units of frequency, suggesting a need to convert to radians per second. There is also a consideration of the scalar nature of speed versus velocity.

Discussion Status

Some participants have provided guidance on checking the units and recalculating using the correct angular frequency. Multiple interpretations of the calculations are being explored, but there is no explicit consensus on the correct answer yet.

Contextual Notes

There is an ongoing discussion about the implications of using different units for frequency and the appropriate mode for calculations on a calculator. The original poster expresses uncertainty about the sign of the speed value.

veitch
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Homework Statement



The position of a mass that is oscillating on a spring is given by x(t) = (14.5cm)cos[(14.0s-1)t].
What is the speed of the mass when t = 0.820 s?

Homework Equations



A= Amplitude
W= Angular frequency

x(t) = ACos(Wt)
v(t) = -WASin(Wt)

The Attempt at a Solution



v(0.820) = (-14.0)(14.5)Sin[(14.0)(0.820)]
= (-203)Sin[11.48]
= -40.4 cm/s

This seems so easy and yet apparently I have the wrong answer... any insight? :/ Thanks in advance
 
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What you did seems right to me.
 
Check the units of your frequency. It looks like you have the value in Hertz (or oscillations per second); try converting the instances of frequency to radians per second (and if you're carrying out the sine calculation on a calculator then change the mode to radians instead of degrees).
 
timmay said:
Check the units of your frequency. It looks like you have the value in Hertz (or oscillations per second); try converting the instances of frequency to radians per second (and if you're carrying out the sine calculation on a calculator then change the mode to radians instead of degrees).

Okay, that makes more sense...

W=2 x pi x freq

thus v(t) = -(2 pi 14)(14.5)Sin[(2 pi 14)(0.82)]

which gives -160 cm/s (with 3 sig figs)... but it still isn't right.
I suppose there shouldn't be a negative should there? Since speed is scalar... but 160 isn't the right answer either. :/
 

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