# (Not so) Simple Harmonic Motion

by XXXXXXX and Jedi Knight Dustin Glazier, February 1999

Here's the quantities you can know:
• X  Displacement
• t  Time
• T  period
• f   frequency
• Vo  Initial velocity
• Va  Average Velocity
• V  Final Velocity
• a  Acceleration
• k  spring constant
• m  mass
• F  Force
• g  gravity

## New Quantities

And here are the formulas that we have so far:

### Defining

El Construction Zone

## Formulas

•

El Construction Zone

## General Problem Solving Strategy:

2. Go through the problem and figure out what is given or implied

3. Make a list, and identify the quantities you know.
4. Find any formula that will allow you to calculate

5. anything that you don't know, and apply it.
6. Add what you just found in the last step to your list of knowns.
7. Check to see if you have found the answer. If not, repeat the

8. previous two steps until you are done.

## Example problem 1

El Construction Zone

## Example problem 2

El Construction Zone

## Sample Problems

el solvedo bi el Jedi Knight Dustin Glazier

```The answers to each problem follow it in parentheses.  They also link to a solution to

the problem.  Try the problem, check your answer, and go to the solution if you do not

understand.

```

## 1.

A spring has a restoring force of 320 N when it is stretched 22.1 cm.  What is the spring's constant k in N/m?
(14.5 N/m)

## 2.

A very stiff spring has a k = 24350 N/m.  What is its restoring force when you distort it 1.00 cm?
(234.5 N)

## 3.

Another totally different spring has a spring constant of 249 N/m.  How far will it distort when you hang a 5.400 Kg mass from it?
(.213 m)

## 4.

A spring has a constant of 34 N/m, and a 3.00 kg mass hangs from it.  What would be the period of motion of the mass on the spring?

## 5.

You need a period of exactly 1.00 seconds, and you have a mass of 230 grams.  What must be the spring constant of the spring?
(.0058 N/m)

## 6.

You need a period of exactly 1.00 seconds, and you have a spring constant of 120. N/m.  What must be the mass on the spring (in grams)? (4700000 grams)

## 7.

Joe takes an unknown spring and hangs a 5.000 Kg mass on it.  The weight of the mass stretches the spring 230.3 cm.  What would you expect the period of the mass to be if it were set in motion? (41 seconds)

## 1.

A spring has a restoring force of 320 N when it is stretched 22.1 cm.  What is the spring's constant k in N/m?
(14.5 N/m)
• X = 22.1 cm
• F = 320 N
• k = ?
• m = ?
• g = 9.8 m/s/s
• T = ?
Well, since we're just starting out, this seems quite easy. We take the formula F = kx, make some slight alterations and voila, we have k = F/X.  An entirly valid equation. Not forgetting to change cm to meters we continue. And like the Glade Plugin's, we plug it in plug it in.  So 320 N / .221 m = k  and k = 14.5 N/m

## 2.

A very stiff spring has a k = 24350 N/m.  What is its restoring force when you distort it 1.00 cm?
(234.5 N)

• X = 1.00 cm
• F = ?
• k = 24350 N/m
• m = ?
• g = 9.8 m/s/s
• T = ?
This is again a matter of plugging, hehehe.  the formula k = F/x works great.  24350 N/m = F / (.01 m).  Boy, this is tough! multiply 24350 by .01 to get kx. WAIT A MINUTE, we shoould have just used F = kx.  At any rate, the answer comes out the same -- 234.5 N

## 3.

Another totally different spring has a spring constant of 249 N/m.  How far will it distort when you hang a 5.400 Kg mass from it?
(.213 m)

• X = ?
• F = ?
• k = 249 N/m
• m = 5.400 Kg
• g = 9.8 m/s/s
• T = ?
Hmmm, I tink that a formula that solves for x would be a good idea!  F/k = x is GRRRRReat!  But we must remember that we don't have F! =(
Fortunately we're brilliant and know that F = mg so mg / k = x.  Put the numbers in and get (5.4 Kg)(9.8 m/s/s)/(249 N/m) = x and therefore x = .213 m!

## 4.

A spring has a constant of 34 N/m, and a 3.00 kg mass hangs from it.  What would be the period of motion of the mass on the spring?
(21.2 seconds)
• X = ?
• F = ?
• k = 34 N/m?
• m = 3.00 Kg?
• g = 9.8 m/s/s
• T = ?
Well, we can use the formula F=kx on this one *sniff, sniff*, but we can use the equation for period, T = 2p(square root of)k/m!!!!!  hmm, what do we do with numbers and an equation? ah yes, plug them in.  so T = 2p(square root of)(34 N/m)/(3.00 Kg) which yields roughly 21.2 seconds.

## 5.

You need a period of exactly 1.00 seconds, and you have a mass of 230 grams.  What must be the spring constant of the spring?
(.0058 N/m)

• X = ?
• F = ?
• k = ?
• m = 230 g
• g = 9.8 m/s/s
• T = 1.00 seconds
I bet the period formula would work splendidly.  T = 2p(square root of)k/m with things plugged is (1.00 sec) = 2p(square root of)k/(.23 kg).  Did you remember to convert the grams to kg...............good.  So work it out, work it out y'all! and you get .0058 N/m, right!?

## 6.

You need a period of exactly 1.00 seconds, and you have a spring constant of 120. N/m.  What must be the mass on the spring (in grams)? (4700000 grams)

• X = ?
• F = ?
• k = 120 N/m
• m = ?
• g = 9.8 m/s/s
• T = 1.00 seconds
Hmmm, I would like to venture a guess, that we should use the period formula.  T = 2p(square root of)k/m plug in what we know.....(1.00 sec) = 2p(square root of)(120)/m.  Seems simple enough.  Doodamaff (do the math) and you get the magically delicous number 4700 kg, but in grams that is 4700000 g.

## 7.

Joe takes an unknown spring and hangs a 5.000 Kg mass on it.  The weight of the mass stretches the spring 230.3 cm.  What would you expect the period of the mass to be if it were set in motion? (41 seconds)