C# Inheritance Question

I need some help setting up an abstract class. Im confused about class variables and how they inherit, if they even do. Spawntime is being treated as a variable shared by all subclasses. Also, is it possible for the child classes to extend on the abstract classes Update() method? Here is the Abstract Class code I have now:

 public abstract class  AbstractProjectile : MonoBehaviour {
 
 
     public bool DestroyOnTimer = false;
     public bool DestroyWhenInvisible = true;
     public float TimeToLiveInSeconds = 1.0f;
 
     
     //Time the Projectile was created
     private float spawnTime;
 
     // Use this for initialization
     void Start () 
     {
         spawnTime = Time.time;            
     }
     
     // Update is called once per frame
     void Update () 
     {            
         //Destroy the projectile if its timer is over
         if (DestroyOnTimer)            {
             
             if ((Time.time - spawnTime) > TimeToLiveInSeconds)
             {
                 Destroy(gameObject);
             }        
         }
         //Call Child projectiles move method
         move();
     }
 
     public virtual void move() { }
   }

Here is the Child Code:

 using UnityEngine;
 using System.Collections;
 
 public class SinBulletScript : AbstractProjectile {
 
     public float speed = 1000.0f;
     public float Amplitude = 600.0f;
     public float Omega = 15.0f;
 
 
     // Use this for initialization
     void Start () 
     {
         Vector3 shipPosition = GameObject.Find("Ship").transform.position;
         shipPosition.y += 100;
         transform.position = shipPosition;
             
         
     }
         
 
     void move()
     {
         gameObject.rigidbody.velocity = new Vector3(Amplitude * Mathf.Sin(Time.time * Omega), speed, 0);
     }
 }