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**Hint:**We know that the maximum value of \[a\sin x + b\cos x\] is \[\sqrt {{a^2} + {b^2}} \] . We will implicate the following formulae. The general equation of a Simple Harmonic Wave is in sin so the above will hold true.

**Complete step-by-step solution**

It is given to us that the equation of the SIMPLE HARMONIC MOTION is

\[y = 3\sin (3.14t) + 4\cos (3.14t)\] .

Here \[a = 3\] and \[b = 4\]

Using \[\sqrt {{a^2} + {b^2}} \]

\[ \Rightarrow Amplitude = \sqrt {{3^2} + {4^2}} = \sqrt {25} = 5\]

The maximum value of the given function is 5 and the maximum displacement in SIMPLE HARMONIC MOTION is the Amplitude of that SIMPLE HARMONIC MOTION.

**Therefore, the answer is option C, 5cm.**

**Note**The theta given inside the cos and the sin functions is equal therefore we are able to apply \[\sqrt {{a^2} + {b^2}} \] . If this were not the case then convert sin function to cos function or vice-versa and then add the corresponding functions to obtain the required value of amplitude.

**Additional Information**Simple Harmonic Motions is a type of periodic motion in which the acceleration of the body is directly proportional to its displacement from the mean position.

With the frequency of oscillations being the constant.

\[a = {\omega ^2}x\]

And its general equation is given by \[x = A\sin (\omega t + \phi )\]

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