need to make this "periodic vx push force " to be specific for each entity. also, would be nice to make the same vx physics for platforms, so they push at left with random periodicity for each specific platform spawned, by not ruining the actual collision system.: class Platform {
  constructor(x, y, w, h) {
    this.x = x;
    this.y = y;
    this.w = w;
    this.h = h;
  }
  collidesWith(obj) {
    if (obj.y + obj.h <= this.y) return false;
    if (obj.y >= this.y + this.h) return false;
    if (obj.x + obj.w <= this.x) return false;
    if (obj.x >= this.x + this.w) return false;

    const objAbove = obj.y + obj.h - obj.vy <= this.y;
    const objBelow = obj.y - obj.vy >= this.y + this.h;
    const objLeft = obj.x + obj.w - obj.vx <= this.x;
    const objRight = obj.x - obj.vx >= this.x + this.w;

    if (obj.vy > 0 && objAbove && !objBelow) {
      obj.y = this.y - obj.h;
      obj.vy = 0;
      obj.jumping = false;
      return true;
    }
    if (obj.vy < 0 && !objAbove && objBelow) {
      obj.y = this.y + this.h;
      obj.vy = 0;
      return true;
    }
    if (obj.vx < 0 && objRight) {
      obj.x = this.x + this.w;
      obj.vx = 0;
      return true;
    }
    if (obj.vx > 0 && objLeft) {
      obj.x = this.x - obj.w;
      obj.vx = 0;
      return true;
    }
    return false;
  }
}

class Player {
  constructor(x, y, w, h) {
    this.x = x;
    this.y = y;
    this.w = w;
    this.h = h;
    this.vx = 0;
    this.vy = 0;
    this.jumping = false;
  }
  move(keys) {
    const friction = 0.9;
    const gravity = 1;
    if (keys[87] && !this.jumping) {
      this.vy -= 20;
      this.jumping = true;
    }
    if (keys[68]) {
      this.vx += 5;
    }
    if (keys[65]) {
      this.vx -= 5;
    }
    this.vx *= friction;
    this.vy += gravity;
    this.x += this.vx;
    this.y += this.vy;
    if (this.x < 0) {
      this.x = 0;
    }
    if (this.y < 0) {
      this.y = 0;
    }
    if (this.x + this.w > canvas.width) {
      this.x = canvas.width - this.w;
      this.vx = 0;
    }
    if (this.y + this.h > canvas.height) {
      this.y = canvas.height - this.h;
      this.vy = 0;
      this.jumping = false;
    }
  }
}

class Projectile {
  constructor(x, y, vx, vy) {
    this.x = x;
    this.y = y;
    this.vx = vx;
    this.vy = vy;
    this.radius = 10;
    this.color = "red";
  }
  update() {
    this.x += this.vx;
    this.y += this.vy;
  }
  draw(ctx) {
    ctx.beginPath();
    ctx.arc(this.x, this.y, this.radius, 0, 2 * Math.PI);
    ctx.fillStyle = this.color;
    ctx.fill();
  }
}

class Entity {
constructor() {
this.x = canvas.width;
this.y = Math.random() * canvas.height;
this.w = 20;
this.h = 20;
this.vx = randomRange(-4, -1); // random initial velocity
this.vy = 0;
this.jumping = false;
this.projectiles = [];
this.color = "blue";
this.period = Math.PI; // period of the periodic vx push force wave
this.minVx = -6; // minimum velocity of the vx push force wave
this.maxVx = -1; // maximum velocity of the vx push force wave
}
  jump() {
    if (!this.jumping) {
      this.vy -= 25 - Math.random() * 25;
      this.jumping = true;
    }
  }
  update(platforms) {
    for (let i = 0; i < platforms.length; i++) {
      platforms[i].collidesWith(this);
    }
    const friction = 0.99;
    const gravity = 1;
    this.vx *= friction; // Fixed the line here.
    this.vy += gravity;
this.x += this.vx;
this.y += this.vy;

// apply periodic vx push force
let t = performance.now() / 1000.0; // current time in seconds
let wave = Math.sin(t * Math.PI / this.period); // calculate the wave value
this.vx = lerp(this.maxVx, this.minVx, (wave + 1.0) / 2.0);
    if (Math.random() < 0.01) {
      this.projectiles.push(
        new Projectile(this.x, this.y, -2 - Math.random() * 6, -2 + Math.random() * 8)
      );
    }
    for (let i = 0; i < this.projectiles.length; i++) {
      this.projectiles[i].update();
      if (
        this.projectiles[i].x < 0 ||
        this.projectiles[i].y < 0 ||
        this.projectiles[i].x > canvas.width ||
        this.projectiles[i].y > canvas.height
      ) {
        this.projectiles.splice(i, 1);
        i;
      }
    }
    if (Math.random() < 0.01) {
      this.jump();
    }
  }
  draw(ctx) {
    ctx.fillStyle = this.color;
    ctx.fillRect(this.x, this.y, this.w, this.h);
    for (let i = 0; i < this.projectiles.length; i++) {
      this.projectiles[i].draw(ctx);
    }
  }
}
// utility function to generate a random number within a range
function randomRange(min, max) {
return Math.random() * (max - min) + min;
}

// utility function to interpolate between two values
function lerp(a, b, t) {
return a * (1.0 - t) + b * t;
}
class Game {
  constructor(canvas) {
    this.canvas = canvas;
    this.ctx = canvas.getContext("2d");
    this.platforms = [];
    this.player = new Player(100, 100, 50, 50);
    this.scrollSpeed = 1;
    this.entities = [];
    this.entitySpawnRate = 0.1;
    this.entitySpawnTimer = 1;
    this.entityIncreaseFactor = 0.1;
    this.keys = {};
    this.platforms.push(new Platform(0, canvas.height - 50, 50, 10));
    for (let i = 0; i < 10; i++) {
      this.createRandomPlatform();
    }
    document.addEventListener("keydown", (evt) => {
      this.keys[evt.keyCode] = true;
    });
    document.addEventListener("keyup", (evt) => {
      delete this.keys[evt.keyCode];
    });
    requestAnimationFrame(this.update.bind(this));
  }
  createRandomPlatform() {
    const x = this.canvas.width;
    const y = Math.random() * this.canvas.height;
    const w = 200 + Math.random() * 500;
    const h = 10;
    this.platforms.push(new Platform(x, y, w, h));
  }
  update() {
    this.player.move(this.keys);
    for (let i = 0; i < this.platforms.length; i++) {
      this.platforms[i].collidesWith(this.player);
      this.platforms[i].x -= this.scrollSpeed;
    }
    for (let i = 0; i < this.entities.length; i++) {
      if (this.entities[i]) {
        this.entities[i].update(this.platforms);
        if (this.entities[i].x < 0) {
          this.entities.splice(i, 1);
          i;
          for (let j = 0; j < this.entityIncreaseFactor; j++) {
            this.entities.push(new Entity());
          }
        } else {
          for (let j = 0; j < this.entities[i].projectiles.length; j++) {
            if (
              this.entities[i].projectiles[j].x > this.player.x &&
              this.entities[i].projectiles[j].x < this.player.x + this.player.w &&
              this.entities[i].projectiles[j].y > this.player.y &&
              this.entities[i].projectiles[j].y < this.player.y + this.player.h
            ) {
              this.player.vy -= 20;
              this.player.jumping = true;
              this.entities[i].projectiles.splice(j, 1);
              j;
            }
          }
          this.entities[i].draw(this.ctx);
        }
      }
    }
    this.player.x -= this.scrollSpeed;
    if (this.platforms[this.platforms.length - 1].x < this.canvas.width - 200) {
      this.createRandomPlatform();
    }
    this.entitySpawnTimer++;
    if (this.entitySpawnTimer >= 60 / this.entitySpawnRate) {
      this.entitySpawnTimer = 0;
      this.entities.push(new Entity());
      this.entitySpawnRate += 0.001;
      this.entityIncreaseFactor = 0.001;
      this.entityIncreaseFactor = Math.min(this.entityIncreaseFactor, 0.001);
    }
    this.ctx.clearRect(0, 0, this.canvas.width, this.canvas.height);
    for (let i = 0; i < this.platforms.length; i++) {
      let p = this.platforms[i];
      this.ctx.fillRect(p.x, p.y, p.w, p.h);
    }
    for (let i = 0; i < this.entities.length; i++) {
      this.entities[i].draw(this.ctx);
    }
    this.ctx.fillRect(this.player.x, this.player.y, this.player.w, this.player.h);
    requestAnimationFrame(this.update.bind(this));
  }
}

let canvas = document.createElement("canvas");
canvas.width = window.innerWidth;
canvas.height = window.innerHeight;
document.body.appendChild(canvas);
new Game(canvas);