Position of an oscillating object

In summary, the equation x = (12.3 cm) cos[(1.26s-1)t] describes the position of an object oscillating on an ideal spring. At t=0.815 s, the object's speed is -13.3 cm/s and the magnitude of its acceleration is -10.1 cm/s^2. It is important to note that the value of 12.3 in the equation is actually 12.3 and not 1.23. Make sure to use radian mode on your calculator when solving for the values. Additionally, this typo does not affect the calculated answers.
  • #1
ChloeYip
93
1

Homework Statement



The position of an object that is oscillating on an ideal spring is given by the equation x =
(12.3 cm) cos[(1.26s-1)t]. At time t = 0.815 s,
(a) how fast is the object moving?
(b) what is the magnitude of the acceleration of the object?

Homework Equations


As follow

The Attempt at a Solution


dx/dt = -12.3*(1.26)sin(1.26*.815) = -0.2777 cm/s but the answer is -13.3cm/sec
dx^2/dt^2= -12.3*(1.26)^2*cos(1.26*.815) = -19.524 cm/s^2 but the answer is -10.1cm/sec^2

I have only little time before test.hope there is someone help me soon.tell me what's wrong with it.
(Please don't ask me to guess... i m not good at that and i really have not time left...)
Thank you very much for helping me
 
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  • #2
##12.3 \ne 1.23## for one thing.
 
  • #3
Thanks for reminding
Thats only multiple of 10, still canet get the answer
Also, the calculated answer is not affect by this typo
Sorry for typo
 
  • #4
Make sure your calculator is in radian mode.
 
  • #5
Ahhh yes
Thanksssssss
 

Related to Position of an oscillating object

What is the position of an oscillating object?

The position of an oscillating object refers to its location at any given time during its motion. It can be measured in terms of distance from a starting point or its displacement from its equilibrium position.

How is the position of an oscillating object affected by its amplitude?

The amplitude of an oscillating object, which is the maximum distance it moves from its equilibrium position, directly affects its position. A larger amplitude means the object will move further from its starting point and reach a higher position.

What is the relationship between the position of an oscillating object and its period?

The period of an oscillating object, which is the time it takes to complete one full cycle of motion, is directly related to its position. As the object moves farther from its equilibrium position, its period will increase.

Can the position of an oscillating object be predicted?

Yes, the position of an oscillating object can be predicted using mathematical equations and principles such as Hooke's law and Newton's laws of motion. These equations can accurately predict the position of the object at any given time during its motion.

How does the mass of an oscillating object affect its position?

The mass of an oscillating object does not directly affect its position. However, it does affect the object's period and amplitude, which in turn can impact its position. A heavier object will have a longer period and may also have a smaller amplitude, resulting in a lower position compared to a lighter object.

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