Observe that the given vector field is a gradient field:
Let
, so that



Integrating the first equation with respect to
, we get

Differentiating this with respect to
gives

Now differentiating
with respect to
gives

Putting everything together, we find a scalar potential function whose gradient is
,

It follows that the curl of
is 0 (i.e. the zero vector).
Answer:
Time, t = 80 seconds
Explanation:
Given that,
The frequency of the oscillating mass, f = 1.25 Hz
Number of oscillations, n = 100
We need to find the time in which it makes 100 oscillations. We know that the frequency of an object is number of oscillations per unit time. It is given by :



t = 80 seconds
So, it will make 100 oscillations in 80 seconds. Hence, this is the required solution.
Answer:
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