Question

question 3 (1 point)
the height h, in centimetres, of a piston moving up and down in an engine cylinder can be modelled by the function ( h(t)=18sin(50pi t)+18 ), where t is the time, in seconds. what is the period?
a) 50 s
b) 0.04 s
c) 0.04 cm
d) 25 s

Explanation:

Step1: Recall the formula for the period of a sine function

The general form of a sine function is \(y = A\sin(Bt - C)+D\), and its period \(T=\frac{2\pi}{|B|}\).

Step2: Identify the value of \(B\) in the given function

In the function \(h(t)=18\sin(50\pi t)+18\), \(B = 50\pi\).

Step3: Calculate the period

Substitute \(B = 50\pi\) into the period formula \(T=\frac{2\pi}{|B|}\). So \(T=\frac{2\pi}{50\pi}\).
Simplify the fraction: \(\frac{2\pi}{50\pi}=\frac{2}{50}= 0.04\) (since the units of \(t\) is seconds, the period \(T\) is in seconds).

Answer:

B. \(0.04\ s\)