How Large is x(t) at Maximum Acceleration for an Oscillating Block?

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In summary, the displacement of an 18.0-kg block oscillating on a frictionless horizontal surface is given by x(t) = (17.0 cm) cos[(22.0 rad/s) t + π rad]. The magnitude of x(t) is maximum when the block experiences its maximum acceleration, which is equal to 17.0 cm. This is because when the acceleration is maximum, the displacement is also maximum. The equation for displacement is given in the problem, with the amplitude (17.0 cm) and angular frequency (22.0 rad/s) already provided. Therefore, the magnitude of x(t) can be easily determined without needing to solve for any other variables.
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shadowice
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Homework Statement


A 18.0-kg block oscillates back and forth along a straight line on a frictionless horizontal surface. Its displacement from the origin is given by
x(t) = (17.0 cm) cos[( 22.0 rad/s) t + π rad]

What is the magnitude of x(t) when the block experiences its maximum acceleration?

Homework Equations


most are below

The Attempt at a Solution


i started to work backwords and solve for k but after that I am lost since i thought k is what i should be solving for

nm just realized it gave it to me in the problem you can delete this
 
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  • #2


What is the magnitude of x(t) when the block experiences its maximum acceleration?
When the acceleration is maximum, x(t) is maximum i.e. a
 
  • #3


ya the original eq had it as the very first term it was 17cm
 

FAQ: How Large is x(t) at Maximum Acceleration for an Oscillating Block?

What is the definition of magnitude in the context of x(t)?

The magnitude of x(t) refers to the size or amplitude of the function x(t) at a specific time t. It is a measure of the strength or intensity of the signal represented by x(t).

How is the magnitude of x(t) calculated?

The magnitude of x(t) can be calculated by taking the absolute value of the function x(t). This means that all negative values are converted to positive values, giving the overall size of the function at a specific time.

What are the units of magnitude in the context of x(t)?

The units of magnitude for x(t) depend on the units of the function itself. For example, if x(t) represents a physical quantity such as displacement in meters, then the magnitude of x(t) would also be in meters.

How does the magnitude of x(t) relate to the frequency of the signal?

The magnitude of x(t) does not directly relate to the frequency of the signal. Frequency refers to the rate at which the signal repeats, while magnitude refers to the strength or intensity of the signal at a specific point in time.

Can the magnitude of x(t) change over time?

Yes, the magnitude of x(t) can change over time. This is because the function x(t) can have different values at different points in time, resulting in a change in magnitude. However, the frequency of the signal remains constant unless otherwise specified.

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