When two SHMs of the same frequency act along the same line, the resultant is also SHM. Use phasor (vector) addition: $A_R = \sqrt{A_1^2 + A_2^2 + 2A_1A_2\cos\delta}$ where $\delta$ is the phase difference. Special cases: $\delta = 0 \Rightarrow A_R = A_1 + A_2$; $\delta = \pi \Rightarrow A_R = |A_1 - A_2|$; $\delta = \pi/2 \Rightarrow A_R = \sqrt{A_1^2 + A_2^2}$. When two SHMs of equal amplitude but slightly different frequencies combine, the result is beats with beat frequency $|f_1 - f_2|$.