A force of 360 newtons stretches a spring 2 meters. A mass of 20 kilograms is attached to the end of the spring and released from the equilibrium position with an upward velocity of 5 meters per second. Find the equation of motion.

Step-by-step explanation:

The statement of the problem shows a case of simple harmonic movement, whose expressions for position is:

An expression for velocity is found by deriving the previous one:

The angular frequency is:

Amplitude and phase angle are found by replacing and simplifying motion formulas:

The equation of motion is:

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

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