SHM一問SHMSHM..................

Your question is quite ambiquous, as there is no description on the simple hatmonic motion (SHM) whatsoever. I could only use some imagination to interpret your question.

Suupose there is an object of mass m, which is fixed to one end of an elastic spring. The other end of the spring is somehow fixed. The whole set up is placed on a smooth inclined plane, with the fixed end of the spring higher up on the slope. The mass thus slides down along the slope, stretching the spring, and eventually will come to rest at an equilibrum position. The extension of the spring is, say xo. Hence, we will have,

mg.sin(theta) = k(xo) -------------------------- (1)
where angle (theta) is the angle of inclination of the slope, g is the acceleration due to gravity, k is the spring force constant.

Now, the mass is made to displace a further distance of x and release, it should perform a simple harmonic motion, as proved below:

net restoring force = mgsin(theta) - k(x+xo)
hence, mg.sin(theta) - k(x+xo) = ma
i.e. mg.sin(theta) - kx - k(xo) = ma
from (1), k(xo) - kx - k(xo) = ma
thus, -kx = ma
a = -(k/m)x
Therefore, the motion is simple harmonic and the angular frequency is given by square-root[k/m]
that is, 2.pi/T = k/m where T is the period and pi = 3.14159...
or T = 2.pi.square-root[m/k]

That is to say, the period T is independent of the inclination angle (theta)

The reason is simple, a constant force ( mg.sin(theta) in this case), applied onto a simple harmonic system will not alter its characterictic parameters, such as frequency and period. It only shifts the equilibrium position. This is generally true.