Answer:

According to the question,

y = 3 sin ωt + 4 cos ωt

Let’s suppose that

3 = a cos φ and 4 = a sin φ

Then, the equation becomes:

y = a cos φ ωt + a sin φ ωt

y = a sin (ωt + φ)

tan φ = 4/3

φ = tan^-1 4/3

When the above equation is squared, we get the following result:

a² = 25

a = 5

Therefore, the new amplitude is 5 cm.