the terrain rises and lowers automatically

If you want to move the entire terrain up and down, a simple solution is to control its transform.position (attach this script to the terrain):

 public range: float = 0.5; // how much terrain swings up and down (meters)
 public speed: float = 6.28; // 6.28 * cycles per second
 
 private p0: Vector3;
 
 function Start(){
   p0 = transform.position;
 }
 
 function Update(){
   transform.position = p0 + Vector3.up * range * Mathf.Sin(speed * Time.time);
 }

But things are way more complicated if you want to move only parts of the terrain: you must somehow define the region you want to move, get the current heights in this region in an square array with GetHeights, modify and assign them back with SetHeights.