What Causes Oscillation Errors in Air-Track Glider Experiments?

[animanga008]

An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at t=0. It then oscillates with a period of 1.50 s and a maximum speed of 46.0 cm/s.

I found the amplitude to be 11cm (this is 100% correct)

1) What is the glider's position at t= 26.0 s?

How do i do #1?

I used the formula x = A cos ( wt) and plugged everything in.

x = (11cm) cos (26sec x 2pie/1.5)
x = -3.56

but my answer is wrong :-(

 

[AlephZero]

Your angle 26*2*pi/1.5 is in radians, but I think your calculator was set to work in degrees.

 

[m2003]

I would first check to see if the units are consistent in the formula being used. The given information provides the period in seconds, but the formula uses radians per second. Therefore, the period needs to be converted to radians per second by multiplying by 2π. This would give a period of approximately 9.42 radians per second.

Next, I would check to see if the amplitude and period values are correct. The given amplitude of 11 cm seems reasonable, but the period of 1.50 s may be incorrect if the maximum speed of 46.0 cm/s is accurate. The period can also be calculated using the maximum speed and the amplitude, using the formula T = 2π√(m/k), where m is the mass of the glider and k is the spring constant.

Assuming the given information is correct, the correct formula to use would be x = A cos (wt + φ), where φ is the phase angle. To find the phase angle, we can use the given information that the glider is released from rest at t=0. This means that at t=0, the glider is at its maximum displacement, which corresponds to a phase angle of π/2.

Plugging in the correct values, we get x = 11 cm cos (9.42 rad/s x 26 s + π/2) = -9.60 cm. Therefore, the glider's position at t=26.0 s is -9.60 cm.

In conclusion, it is important to double check the units and values used in the formula, and to use the correct formula for the given situation. It is also helpful to have a good understanding of the physical concepts involved in the problem to check for any inconsistencies.