Position of an oscillating object

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The position of an oscillating object on a spring is described by the equation x = (12.3 cm) cos[(1.26 s^-1)t]. At t = 0.815 s, the user attempts to calculate the object's velocity and acceleration but receives incorrect results. The user initially calculates the velocity as -0.2777 cm/s and acceleration as -19.524 cm/s², while the expected answers are -13.3 cm/s and -10.1 cm/s², respectively. A key issue identified is the need to ensure the calculator is set to radian mode for accurate results. The discussion emphasizes the importance of correct unit handling and calculator settings in solving oscillation problems.
ChloeYip
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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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##12.3 \ne 1.23## for one thing.
 
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
 
Make sure your calculator is in radian mode.
 
Ahhh yes
Thanksssssss
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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