Simple SmartApp that turns a light on with motion, and off when no motion has been detected for a certain time period.

turn-on-with-motion-off-after-specified-time.groovy

/**
 *  Text Me When There's Motion
 *
 *  Author: SmartThings
 */
definition(
        name: "My First SmartApp",
        namespace: "mygithubusername",
        author: "Peter Gregory",
        description: "This is my first SmartApp. Woot!",
        category: "My Apps",
        iconUrl: "https://s3.amazonaws.com/smartapp-icons/Convenience/Cat-Convenience.png",
        iconX2Url: "https://s3.amazonaws.com/smartapp-icons/Convenience/Cat-Convenience@2x.png",
        iconX3Url: "https://s3.amazonaws.com/smartapp-icons/Convenience/Cat-Convenience@2x.png")

preferences {
	section("Turn on when motion detected:") {
    	input "themotion", "capability.motionSensor", required: true, title: "Where?"
    }
    section("Turn off when there's been no movement for") {
    	input "minutes", "number", required: true, title: "Minutes?"
    }
    section("Turn on this light") {
    	input "theswitch", "capability.switch", required: true
    }
}

def installed() {
	initialize()
}

def updated() {
	unsubscribe()
	initialize()
}

def initialize() {
	subscribe(themotion, "motion.active", motionDetectedHandler)
    subscribe(themotion, "motion.inactive", motionStoppedHandler)
}

def motionDetectedHandler(evt) {
	log.debug "motionDetectedHandler called: $evt"
    theswitch.on()
}

def motionStoppedHandler(evt) {
	log.debug "motionStoppedHandler called: $evt"
    runIn(60 * minutes, checkMotion)
}

def checkMotion() {
	log.debug "In checkMotion scheduled method"
    
	def motionState = themotion.currentState("motion")
    
    if (motionState.value == "inactive") {
		// get the time elapsed between now and when the motion reported inactive       
        def elapsed = now() - motionState.date.time
        
        // elapsed time is in milliseconds, so the threshold must be converted to milliseconds too
        def threshold = 1000 * 60 * minutes

		if (elapsed >= threshold) {
            log.debug "Motion has stayed inactive long enough since last check ($elapsed ms):  turning switch off"
            theswitch.off()
    	} else {
        	log.debug "Motion has not stayed inactive long enough since last check ($elapsed ms):  doing nothing"
        }
    } else {
    	// Motion active; just log it and do nothing
    	log.debug "Motion is active, do nothing and wait for inactive"
    }
}