# Simple Harmonic Motion of an air-track glider

saralsaigh
I have several questions i will write all of them and give you my attempt at a solution, hope you can help me figure out what i am doing wrong, Thanks.

Question 1:
An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at t=0.00 s. It then oscillates with a period of 11.4 s and a maximum speed of 52.9 cm/s. What is the glider's position at t=0.561 s?
T = 11.4s, Vmax = 52.9 cm/s
I found out W (angular frequency) to = 0.175 pi = 0.55498 rad/s
I also found A = 96.22 cm I used the equation
X(t) = A cos ( w t )
X(0.561) = (96.22) cos ( 0.55498 x 0.561 )
= 96.2186 cm
apparently this is the wrong answer....idk wat i am doing wrong though..any pointers?

Question 2:
A 543.0 g mass oscillates with an amplitude of 12.4 cm on a spring whose spring constant is 27.3 N/m. At t=0.00 s the mass is 4.36 cm to the right of the equilibrium position and moving to the right. Determine the phase constant. Use a cosine function to describe the simple harmonic motion.
Knowns: Xinitial = 4.36 cm A= 12.4 cm
phase constant = cos^-1 ( Xinitial / A )
= cos^-1 (4.36 / 12.4)
Again i got the wrong answer and idk where i went wrong....

Question 3:
An object in simple harmonic motion oscillates with a period of 4.00 s and an amplitude of 9.79 cm. How long does the object take to move from x=0.00 cm to x=6.50 cm?
Knowns: T=4s A= 9.78m
I found: w= 2pi/ T = 0.3927 rad/s
Vmax = wA = 3.845 cm/s

Question 4:
The velocity of an object in simple harmonic motion is given by v(t)= -(0.226 m/s)sin(15.0t + 2.00π), where t is in seconds. What is the first time after t=0.00 s at which the velocity is -0.110 m/s?
==> ANSWER: so since the equation for velocity is
V(t) = -(Vmax) sin ( wt + phase constant )
we know that,
i figured that the speed would be the same after a period....so i set out to find the period,
T = 2pi / w = 0.4189s
however that is the wrong answer, is there a flaw in my logic?

Question 5:
A 6.00 g spider is dangling at the end of a silk thread. You can make the spider bounce up and down on the thread by tapping lightly on his feet with a pencil. You soon discover that you can give the spider the largest amplitude on his little bungee cord if you tap exactly once every 7.00 s seconds. What is the spring constant of the silk thread.
m= 6g = 0.006 kg
T= 7s
k = ?
I used the equation T = 2pi ( m / k )^(1/2)
i rearranged it for k = (m 4pi) / T^2 = 1.54 x 10^-3 N/m
again this was the wrong answer....plz help.

Sry for posting so many questions but i didnt want to start many threads and the topic is all related its just that im studying for a test and these are the questions im stuck on....any help would be greatly appreciated..THANKS AGAIN!

xboy
1.The physics part seems to be correct.However i'm getting something like 91 as the answer.if that is close to the correct answer you need to check your calculations,put exact value of pi and stuff.

3.you know x as a function of t.so you can write t as a function of x.take it from there.

4.Are you sure you have got the equation correct?anyways have you tried using the formula directly?

5.You made a mistake while rearranging.check it.

saralsaigh
1.The physics part seems to be correct.However i'm getting something like 91 as the answer.if that is close to the correct answer you need to check your calculations,put exact value of pi and stuff.

3.you know x as a function of t.so you can write t as a function of x.take it from there.

4.Are you sure you have got the equation correct?anyways have you tried using the formula directly?

5.You made a mistake while rearranging.check it.

1- yea i wasnt in radian mode ...THANKS
2- I tried it in radian and i got 1.212 and its also wrong :S
3- i can rearrange the x(t) equation to have it as a function of t but i have two x's.....im confused...
4- yea i believe its the rite equation and i did try it and i got the same answer
5- i couldnt find my mistake so i just plugged in the numbers and then rearranged and i still got the same answer :/

xboy
2.how can that be wrong??i'm stumped.
3.how would you do it if you were to calculate the distance travelled b/w say,t=1 and t=2?think a bit and i'm sure you'll find a way.
4.the same answer??what you've found there is just the time period of the shm.
remember that a 2pi phase change gives the same value of sine function.i'm getting a much lower value - less than 1/10th of your value.is that correct?
5.yet there is a mistake.something you didn't square...