MediumMathematicsHigh School (11–12)Functions and Calculus › Limits and DerivativesNumerical

The displacement of a vibrating plate is y = t²sin t centimetres (cm), where t is the time in…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

The displacement of a vibrating plate is $y = t^2\sin t$ centimetres (cm), where $t$ is the time in seconds (s) and the angle $t$ in the sine is in radians. The amplitude grows with time. Find the displacement at $t = \dfrac{\pi}{2}$ s, to three decimal places. Then use the product rule to find the rate of change of the displacement at that instant, to four decimal places.

Need a reminder? The key ideaShow

Product rule: $(uv)' = u'v + uv'$ . Quotient rule: $\left(\dfrac{u}{v}\right)' = \dfrac{u'v - uv'}{v^2}$ . The derivative $\dfrac{dy}{dx}$ is a rate of change, in units of $y$ per unit of $x$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

← All Problems

← PreviousThe cost per unit of a process is modelled by g(x) = (x² + 1)/(x - 1) for x > 1, where x is the… →

More onFunctions and Calculus › Limits and Derivatives

Discussion (0)

Loading…